"If a Pokémon with Flame Body (or Magma Armor or Steam Engine) and a Pokémon Egg are both in the party Pokémon, the number of steps required to hatch the egg are halved." - Pokemondb
"From Pokémon Emerald onward, if a Pokémon with Flame Body is in the party (even if fainted), the number of cycles it takes for all Pokémon Eggs in the party to hatch are halved. This effect does not stack with itself, Magma Armor, or Steam Engine; however, it can be stacked with Hatching Power Pass Power, O-Power, or Roto Hatch." - Bulbapedia
No. Ever since Gen 3 when abilities were first introduced Flame Body has not required that the Pokemon be next to an egg in the party, just that it needs to be in the party with the egg.