The Blissey kill themselves with Healing Wish so you don't have to worry about killing them, just saying...
Even if you were to kill them yourself with Brave Bird / Flare Blitz, Talonflame would die real quick from the recoil it would take due to Blisseys massive HP stat
The last Blissey can't kill herself, as Healing Wish doesn't work if the user is the only pokemon alive in the team.
Also, to answer
mirage_drag0n's question, wouldn't itemless Acrobatics work? It doesn't have recoil, unlike Brave Bird and Flare Blitz, and I don't think Talonflame needs to have an item to do its egg-hatching job. Acrobatics should do this to the last Blissey:(although I'm not sure about their EVs/nature)
252+ Atk Talonflame Acrobatics (110 BP) vs. 0 HP / 0 Def Blissey: 604-712 (92.7 - 109.3%) -- 56.3% chance to OHKO
And worst-case scenario:
252 Atk Talonflame Acrobatics (110 BP) vs. 252 HP / 252+ Def Blissey: 237-280 (33.1 - 39.2%) -- 100% chance to 3HKO <- not really 100%, because 237*3 = 711 and Blissey's max HP is 714, but it's guaranteed with poison damage from the Toxic Orb
However, guessing which Blissey will lose the speed tie(assuming there is one, ofc) and use Healing Wish last(and therefore fail) is hard:/ Unless people start giving nicknames to the slowest one <- actually not a bad idea