To check how compatible your Pokemon are, talk to the Old Man. Depending on what he says, the chance of an Egg being produced can be determined. (Info from Super Creatures)
The two seem to get along very well = Same Pokemon Species and different Original Trainer = ~69.3% chance of an egg being made after 256 steps.
The two seem to get along = Same Pokemon Species and same Original Trainer or Different Pokemon Species and different Original Trainer = ~49.5% chance of an egg being made after 256 steps.
They don't seem to like each other very much = Different Pokemon Species and different Original Trainer = ~19.8% chance of an egg being made after 256 steps.
The two prefer to play with other Pokemon than each other = Not in the same Egg Group, Pokemon is unbreedable, or both Pokemon are the same Gender = 0% chance of an egg being made after 256 steps.
The Flame Body/Magma Armor trick and Everstone trick do not work in FireRed/LeafGreen; they were first introduced in Emerald.