Let me try-
1. Stealth Rock + Priority
I know SR is not popular in Doubles, but after SR, Talonflame loses 50%, and it can be taken out with priority. Any good Stealth Rock setter who can take hits will work, but I'm listing Empoleon.
Empoleon @ Leftovers
Ability: Torrent
EVs: 248 HP / 8 SpA / 252 SpD
Calm Nature
- Stealth Rock
- Protect
- Flash Cannon
- Icy Wind
Now you need priority, the best Pokemon for the job is-
Lucario @ Lucarionite
Ability: Inner Focus
EVs: 252 Atk / 4 SpD / 252 Spe
Jolly Nature
- Extreme Speed
- Swords Dance
- Substitute
- Bullet Punch
+2 252 Atk Mega Lucario Extreme Speed vs. 120 HP / 0 Def Talonflame: 250-295 (76.4 - 90.2%) -- guaranteed OHKO after Stealth Rock
2. Rock-types
Tyranitar @ Tyranitarite
Ability: Sand Stream
EVs: 252 HP / 252 Atk / 4 SpD
Adamant Nature
- Rock Slide
- Crunch
- Earthquake
- Protect
Tyranitar is a great counter because it resists Talonflame's STABs and can KO it with one Rock Slide. Preferably pair it wit something that has Protect or is Flying-type.
If I think of some more, I'll add them later.