I came up with these numbers using just my recent experience. Many factors such as my opponents' skill levels, sideboard cards, etc. could result in me being wrong on a few of these.
Hogaak: 50/50. If I had to choose a winner in this matchup, I'd say Hogaak more consitently draws god hands than Burn; however, the margin is close enough for me to call it even. Whoever loses the die roll in this matchup should be sweating bullets.
Burn: 50/50 (obviously). If you plan to take Burn to the GP, and you don't have much experience with it, I'd recommend searching around for other Burn players' descriptions of how the matchup goes and how you should approach it.
Izzet Phoenix: 60/40. Remember when I said it's hard to hate on Izzet Phoenix? Eidolon of the Great Revel is an exception, Phoenix cannot win through Eidolon unless they are already ahead. This alone puts Burn at an advantage. Additionally, the matchup is basically 50/50 even without Eidolon and Burn has better sideboard cards.
Mono Red Phoenix: 60/40. Don't make the mistake of assuming Mono Red Phoenix is basically Izzet Phoenix with some minor differences. Arclight Phoenix is merely a backup plan in this deck, which aims to kill with Prowess creatures 80% of the time. With that said, Lightning Helix and Searing Blaze are better than any mainboard card in Phoenix. Try to board in a piece of artifact hate or two because these decks are notorious for running Dragon's Claw.
Eldrazi Tron: 50/50. Yeah, Chalice is great against Burn but sometimes it doesn't lock out enough spells by the time it comes down. Eldrazi can just as easily get overrun, especially if it loses the die roll. Thought-Knot is a great creature in the matchup but it can't block spells that fly directly to the face. I'd call this one even.
Humans: 50/50. I've heard players of both these decks complain about this matchup, and for good reason. They're both packed with mainboard cards that are great in the matchup, from Thalia to Searing Blaze, Freebooter to Lightning Helix. You just have to hope your draws line up well against theirs. Remember to respect the sideboard Auriok Champions.
Tron: 55/45. I had recently begun to lose more matches to Tron once Karn, the Great Creator as printed, mostly because Trinisphere kept coincidentally locking me down. However, a lot of lists aren't even playing that card anymore. Additionally Tron can't do a single thing if they get killed on turn 3, which we can sometimes pull off. The matchup is still fairly good, possibly even better than I give it credit for.
Jund: 55/45. Jund has been running smooth as butter recently thanks to their new 2 mana planeswalker but I think Burn still has the speed to kill them a little more often than they have the cards to stabilize.
U/W: 40/60. Some Burn players claim this matchup is good. I believe it used to be, but it plays a lot lower to the ground than before and a lot of lists are prepared to fight aggro. Being as I didn't fit any Skullcracks or Exquisite Firecrafts in my sideboard this time around, I have effectively forfeit the result of this match to luck, as I don't believe either of those cards improve the matchup by a wide enough margin. I am at peace with this fact since I like my sideboard against every other big deck in the format.
Whirza: 55/45. There are quite a few x/4 creatures in this deck that don't die to a single bolt but Searing Blaze combines with pressure from attacking creatures can often trap them after they block. Since the archetype is low on removal, I really want to try to race this deck more than anything. They're generally the slower deck.
Hardened Scales: 45/55. This matchup could also be close to even but Arcbound Ravager is just a headache. I would try to control the ground in this matchup as much as you can so our creatures can get in for as much damage as possible. Then Burn their face and hope they die before you get to 10 poison of 0 life.