There are many ways to beat talonflames. Mono fighting has Terrakion and Coballion to counter it. Mono grass has cradily. I think a more pressing issue in the monotype tier is Swift Swim
The best Bug counter to Talonflame is Shedinja :P
Seriously though, fully physically defensive Cobalion takes over a third from switching in on a Brave Bird:
252+ Atk Choice Band Talonflame Brave Bird vs. 252 HP / 252+ Def Cobalion: 142-168 (36.7 - 43.5%) -- 99.1% chance to 3HKO after Leftovers recovery
252+ Atk Life Orb Talonflame Brave Bird vs. 252 HP / 252+ Def Cobalion: 122-146 (31.6 - 37.8%) -- 0.2% chance to 3HKO after Leftovers recovery
Which means Talonflame can then kill it with a Flare Blitz if it's LO:
252+ Atk Life Orb Talonflame Flare Blitz vs. 252 HP / 252+ Def Cobalion: 244-291 (63.2 - 75.3%) -- guaranteed 2HKO after Leftovers recovery
252+ Atk Choice Band Talonflame Brave Bird vs. 252 HP / 252+ Def Cobalion: 142-168 (36.7 - 43.5%) -- 99.1% chance to 3HKO after Leftovers recovery (for the sake of being thorough)
So that's Cobalion, with 91/129 defenses, almost always getting 3HKO'ed if not 2HKO'ed by Talonflame (if you add the LO values, it comes out to 386 total getting minimum damage both times.).
However, it can OHKO Talonflame with uninvested Stone
Miss Edge. But there are a few problems with this:
1) Talonflame outspeeds Cobalion at just max speed even when Cobalion is max speed+Jolly. This means that it can KO Cobalion with a Flare Blitz before Cobalion has a chance if it's LO.
2) If Talonflame is CB, it can simply switch out in most situations. Sure, most Fire or Flying types are weak to Stone Edge, but it's not often that you see a MonoFire team without Infernape or Heatran or a MonoFlying team without Gliscor or Skarmory.
3) Stone Edge just has downright shoddy accuracy, whereas Talonflame is going to hit each and every one of its moves.
4) Talonflame has priority Roost, which is another option for LO sets. This also decreases the weakness to Stone Edge to only 2x.
I'll post stuff and things for Cradily and Terrakion later, that took a long time. Anyway, I hope this was helpful, it was my first real post ^.^
EDIT: Alright, here's Terrakion:
Brave Bird:
252+ Atk Choice Band Talonflame Brave Bird vs. 252 HP / 252+ Def Terrakion: 181-214 (46.8 - 55.4%) -- 72.7% chance to 2HKO
252+ Atk Life Orb Talonflame Brave Bird vs. 252 HP / 252+ Def Terrakion: 157-187 (40.6 - 48.4%) -- guaranteed 3HKO
Flare Blitz (to compare with Cobalion):
252+ Atk Choice Band Talonflame Flare Blitz vs. 252 HP / 252+ Def Terrakion: 90-107 (23.3 - 27.7%) -- 78.7% chance to 4HKO
252+ Atk Life Orb Talonflame Flare Blitz vs. 252 HP / 252+ Def Terrakion: 78-94 (20.2 - 24.3%) -- guaranteed 5HKO
So Terrakion seems to be the most solid counter to Talonflame, but most of them aren't going to be running max Defense+HP, so the calcs that Treecko posted above for Terrakion are probably more relevant.
And Cradily:
252+ Atk Choice Band Talonflame Brave Bird/Flare Blitz vs. 252 HP / 252+ Def Cradily: 172-204 (45.7 - 54.2%) -- 4.7% chance to 2HKO after Leftovers recovery
252+ Atk Life Orb Talonflame Brave Bird/Flare Blitz vs. 252 HP / 252+ Def Cradily: 149-177 (39.6 - 47%) -- guaranteed 3HKO after Leftovers recovery
I grouped the Brave Bird and Flare Blitz calcs together because they do exactly the same damage to Cradily (but you should probably go for Flare Blitz for the 10% burn chance to be a troll).
Here are the calcs for Crustle, the most physically bulky Bug (Dwebble with Eviolite actually has 2.5 more in defense, but there's a difference of 20 base HP. I'm not going to bother calcing it because the difference isn't too big and they can both OHKO with Stone Edge.) who takes neutral damage from both Brave Bird and Flare Blitz & can kill it back with a Rock STAB (happy?):
252+ Atk Life Orb Talonflame Brave Bird/Flare Blitz vs. 252 HP / 252+ Def Crustle: 126-149 (36.6 - 43.3%) -- 97.3% chance to 2HKO after Stealth Rock
252+ Atk Choice Band Talonflame Brave Bird/Flare Blitz vs. 252 HP / 252+ Def Crustle: 145-172 (42.1 - 50%) -- guaranteed 2HKO after Stealth Rock
Oh right, there's Shuckle. Well the calcs are below.