You might here some talk about how RDW/Burn is gutted, but I'm here to show you that those claims are overblown. To put it bluntly, those people can't play burn in the first place. If mono red was as easy as people think, then every scrub would play it (instead, scrubs play Rhinos).
Burn lost three important cards: Lightning Strike, Searing Blood, and Eidolon of the Great Revel. Of the three, Eidolon is going to hurt the most. Searing Blood will hurt a little, and you won't miss Lightning Strike at all. Here is my decklist for this expansion, and it has already gone 4-0 at one event; this is how we do it:
4x Monastary Swiftspear
4x Hangarback Walker
4x Abbot of Keral Keep
4x Thunderbreak Regent
2-3x Chandra, Fire of Kaldesh
2-3x Mage-Ring Bully
4x Fiery Impulse
4x Wild Slash
4x Exquisite Firecraft
3x Titan's Strength
3x Temur Battle Rage
4x Arc Lightning
2x Smash to Smithereens
4x Flamewake Phoenix
Xx Rest of your Titan's Strengths, Temur Battle Rages, Chandras, Smash to Smithereens, Mage-Ring Bullies
4x Infectious Bloodlust
The Thunderbreaks are your coffin nails. Keep four in the mainboard for most matches. He's that good (the same goes for Swifty, Abbot, Wild Slash, and Exquisite). Chandra, the Bully, and the Phoenixes can all be adjusted in the sideboard phases. You don't want the phoenixes if your opponent has a lot of fliers. You don't want bullies when your opponent can force you into bad combat (actually not as common as you think). You don't want Chandra when your opponent is packing too much burn or counters. I always keep at least 2 Chandras in my deck online (via Cockatrice), but at FNM I play with 3. Against a very aggressive counter deck, I might drop even more in favor of phoenixes.
Hangarback and the Bully fill the void left by Eidolon of the Great Revel. At least he finds a home in modern burn, but actually Hangarback is exactly what we want. First, he drops for 2, which the curve here really needs. Second, he can mana-sink, which means you don't need Lightning Berserker. I like Lightning Berserker, but he's very bad right now and doesn't play nice with the deck. Third, the flying tokens put extreme pressure on the opponent, and can save the game when Radiant Flames would wipe your board. Just run the fucker, it is a beast. Learn to tap him for a counter in response to stuff that would kill him and at end of turn.
The Mage-Ring Bully seems like a bad card, but he isn't. Two mana, solid 2/2, and prowess is a force to be reckoned with. His downside is only a downside if your opponent has creatures. We solve this problem with our slashes and impulses.
You can't play Abbot on Turn 2, as it is almost universally a bad move. Statistically, you want to use him to mill through more of your deck so that you draw and can use more of your cards.
Fiery Impulse and Wild Slash give you 8x 1-mana removals. You will shred them. De-board an impulse or two if your opponent isn't running creatures, but I don't know of any standard deck without creatures.
Exquisite Firecraft is best saved as a finisher. Generally the rule of thumb is you don't want to be using these guys on removal, but this will depend upon the math of the board state and your intuition. Of course there are exceptions: you have to clear something like Soulfire Grandmaster, and you should do it quickly. All hope is not lost if you have to use all your Firecrafts, you just push the game into topdeck mode, hoping to pull Hangarback, Flamewake, Firecraft, or Thunderbreak.
Titan's Strength, Infectious Bloodlust, and Temur Battle Rage are all great cards even if they aren't as straightforwardly awesome as Searing Blood (which, also good for modern). I have dropped Infectious Bloodlust from my deck, but I don't think it's a bad card or choice. I just found the instant-speed combat tricks to be more useful in practical application. Play both tricks at once, on the same guy, and you swing your Bully for 14. Swifty for 12. This is turn three. Your creature is probably buff enough to survive the blocker and trample over plenty of damage. Or, if prowess will be enough to survive the block, play them on the unblocked creature.
Arc Lightning can be your savior. If they play elves, tokens, Jeski, aggro, goblins, thopters, whatever, then bring these into play. You probably have to drop a bully and some combat tricks.
Pilot the Deck
Prowess lets you stack aggro damage. If you get an opening (i.e. unblocked creature) Go ahead and play Titan's Strength if the scry would be useful and you don't also have Temur Battle Rage. Those two cards are your god-combo, so don't throw away half of the set lightly. Likewise, you want to always kind of hope for a Thunderbreak swing with Temur Battle Rage.
Keep clearing those creatures with wild slash and fiery impulse. Don't use wild slash for face damage unless you know for sure that you can win. You will lose the game if you opponent keeps his Soulfire Grandmaster, Seeker of the Way, or Drana for too long.
On that note, don't neglect spell mastery for fiery impulse. It's often best to use wild slash first, even though it can attack the face, because impulse will now clear mantis riders and other strong dudes.
Don't let managorger hydra suvrive at all. Same for Hangarback, Chandra, Nissa, Jace, Lilliana, anything with lifelink, etc. Really don't let anything live. Maybe a token. You might have to let elves live too, if you think they have a better elf.
Planning for Your MetaBecause I'm thinking of many different metas here, you'll want to tailor your deck for your own environment. For example, no one ever runs Abzan at my local game shop, so I don't even sideboard roast. If you know there are rhino decks, even a mainboarded set of 2x roasts wouldn't be out of the question.
First, if your meta is very powerful, I would run two Chandras and 3 Bullies. I run 3 Chandras and 2 Bullies at mine, as it is a much weaker environment than cockatrice (see; www.woogerworks.com).
Knowing a store's meta is usually not too hard for mono red, as you will have plenty of time to glance at other players' games with all your free time. Don't think about it too hard, however, and don't neglect to run the essential cards (including Hangarback walker and Chandra) until the next set.
Expect fiery impulse and wild slash to always be in the deck as well, there will be plenty to burn in this meta. Not sure there is anything wrong with packing the Hangarbacks Walkers through this set and reaping the rewards of victory. The card is stupid good.
Your Worst NightmareRadiant Flames. Board wipes. Other Thunderbreak Regents. You don't want to overextend yourself to getting wiped. Similarly, sometimes it might be better to ping them a few times without your combat tricks instead of inviting the kill-spell early on. This, however, is all in the mind-reading aspect of MtG, so judge your opponent well and don't play into his/her hand.
With that said, don't be afraid to take a chance! You are MONO RED! The red deck always wins*
Putting It all Together: Robot's Red Deck Wins
Here is the deck I play online. At FNM I used 3 Chandras and 2 Bullies in the mainboard, anticipating being able to flip her (which happened often, leading to many wins).
4 Monastery Swiftspear
4 Exquisite Firecraft
4 Abbot of Keral Keep
4 Wild Slash
4 Fiery Impulse
4 Thunderbreak Regent
2 Chandra, Fire of Kaladesh
3 Titan's Strength
3 Temur Battle Rage
3 Mage-Ring Bully
4 Hangarback Walker
SB: 4 Arc Lightning
SB: 2 Smash to Smithereens
SB: 1 Mage-Ring Bully
SB: 1 Zurgo Bellstriker
SB: 1 Chandra, Fire of Kaladesh
SB: 4 Flamewake Phoenix
SB: 1 Titan's Strength
SB: 1 Temur Battle Rage
I wonder if the extra tricks are useless, however, and if I would be better off with roast. I just can't see myself swapping roast into the deck, same for draconic roar--I'd rather have fiery impulse. If they pack hate for artifacts and have strong fliers, however, I could see needing more combat tricks.
The other reason for the inclusion of the 4th Temur Battle Rage is that I'm not sure if this card is actually just fucking broken or what. I feel like it probably is really amazing, but I don't know what to take out.
I am confidant that this amount of creatures is needed in order for the deck to go off. Two less creatures and losing a dude becomes losing the game very often. Hangarback gives us some lingering effects, which we really wanted. Hangarback is just good fun and solves many problems for us. He's also a 4-drop if we have the mana, so no longer do we just rely on topdecking a dragon. It really is perfect. Bully gives us some cheap, serious threats that also works very, very with every one of our spells.
Zurgo doesn't do enough for us. He can't chump, so he basically has to attack to be useful. Bully also has to attack, but he has prowess. Your opponent might also let the bully slide, knowing she can kill it in two turns, but it will be two late. You slap down Titan and Temur for 14 dmg and your Swifty swings for 3.
We aren't going to have an delusions of winning on T3 most of the time. We will have the momentum, but the win will have to come on T5-6 for most games. That's just standard, and it's the price we pay for Thunderbreak Regent.
*the red deck does not always win, but it wins a lot.