I can only think of 3 cases. Note: Flame Body and Magma Armor both halve the number of steps needed for the Egg to hatch. The Big Pecks Fletchling would have originally evolved into a Flame Body Fletchinder/Talonflame and the place the Fletchling was originally from doesn't matter, so there's nothing wrong with it.
- The effects don't stack so 1 Flame Body/ Magma Armor Pokémon=same effect as 2 Flame Body/Magma Armor Pokémon. You might have thought the effects of the abilities stack, and assumed the ability didn't work
- The Slugma has neither Flame Body nor Magma Armor. Since you got that Slugma through DexNav, it could have a chance of getting it's Hidden Ability Weak Armor and not its normal abilities Flame Body or Magma Armor
- As DA830 said, you were hatching a different Pokémon. Each Pokémon takes a different number of steps and Egg Cycles to hatch. You should try with the same type of Pokémon.
Source: Pokédex pages of Fletchling, Talonflame, Slugma, Magma Armor and Flame Body