I have a Magcargo and Talonflame hatching eggs, and I feel like I may be wasting a party member.
In Pokémon Emerald and all subsequent games, it also halves the number of cycles it takes for an Egg to hatch. Both the Pokémon with Flame Body and the Egg must be in the party in order for this to work. Magma Armor also has the same effect. However, this effect will not stack up if multiple Pokémon with Flame Body and Magma Armor are in the party.
Source