Counter: Switches in on any move and then kills or forces a switch.
Check: Comes in after a pokemon died to revenge kill, or, is able to switch in on some but not all possible moves.
Counters:
Heatran, especially physically defensive heatran, is probably the best counter. But some Talonflames use Roost, so you probably need to carry Earth Power or Hidden Power Rock or Ancient Power or Roar to actually beat it. Use the opportunity to set up stealth rock, then use the move of choice to kill it or roar it out.
Tyranitar, comes in and causes sandstorm, which will tell you if it is using leftovers or not. Has many options to kill talonflame, including stone miss, thunderbolt, and dark STABs. Susceptible to u-turn.
Hippowdon with maximum hp and defense takes 65 - 76.66% from a +2 Gem Acrobatics, or, 35.71 - 42.14% from two CB Brave Birds. Needs stone miss to get the kill though.
Rhyperior, Golem, Gliscor, Donphan, Regirock, eviolite Rhydon, and Gigalith function similarly. Some of them have the 100% accurate Smack Down to use, or the more rewarding Head Smash.
Slowbro at near maximum defenses takes 31.47 - 37.05% from CB u-turn, or, 39.84 - 47.2% from CB Brave bird, or, 73.09 - 86.04% from +2 Gem Acrobatics.
Gyarados, maximum defensive bulk gyarados with intimidate and leftovers. Switches in and intimidates talonflame, who may have possibly used Swords Dance. +1 Flying Gem Acrobatics does 68.02 - 80.2%, but waterfall kills it in return. Two -1 CB Brave Birds does 32.99 - 39.08% x2. Leftovers are important to avoid SR.
Salamence, (maximum defensive bulk with leftovers) functions just like gyarados, it even has the same base HP and almost exactly the same base defense. Survives +1 Gem Acrobatics and ohkos back.
Landorus-T is similar. Slightly lower base HP but slightly higher base Def. Crucially is only neutral to SR, meaning it does not need leftovers
Mandibuzz: maximum defense bulky takes 70.21 - 82.97% from +2 flying gem acrobatics and ohkos back with Foul Play
Umbreon would take 73.09 - 86.04% from +2 gem acrobatics and ohko back with Foul Play
Rotom-W or Rotom-H, if you invest in some defences then you can handle anything it does to you and ohko back with hydro pump or thunderbolt or possibly voltswitch.
Aggron, with maximum hp and defense, takes 31.68 - 37.79% from CB Flareblitz or 54.65 - 65.11% from +2 LO Flare Blitz
Kabutops switches in to anything and ohkos
Omastar, Carracosta, Relicanth, and Barbacle do the same.
Ampharos at maximum defenses takes 52.6 - 61.97% from CB Flare Blitz when it switches in, followed by like 25% after it megaevolves and ohkos with STAB