itch.io

There's no breeding mechanic built in. It probably wouldn't be TOO hard to add one, but still pretty involved:

• Set up "egg groups" and assign monster species to them. Not sure what's the best way here, but since you won't check them very often you don't need to worry about performance.
• Add a daycare (or somesuch) where you can deposit monsters. Easiest way would be to functionally add a new storage box, which can't be accessed from the shrine PCs. Every time the player takes a step, you could loop over every monster in this box and give them EXP (if you wanna copy Pokémon wholesale), but you'd also tick up some daycare counters every time you reach a step threshold (256 or something)
• When monsters of a matching egg group are in the daycare, each Egg Tick you'd roll a random number to see if it's time to create an egg. 
• I think the easiest way would be to have an "egg flag" in the AMP data, which is true for eggs and false for other monsters. If the egg flag is true, the monster is considered fainted (so it can't be sent out) and checking its status will give you a special screen with the hatching info. The moment you generate an egg in the daycare, you actually generate the lowest evolution of the mother (and put it in another slot in the Daycare Box - or if you want to be able to generate more than one egg at a time, you might want to have a special Egg Box instead), and then just sets its egg flag to true. (You could also manually overwrite data for things like inheriting IVs, Egg Moves and so on)
• If the player has any eggs in the party, you'd reduce the hatch counter for every egg in the party every Egg Tick, and if an egg hits zero, abort the loop and go to a hatching sequence (which you'd handle similar to how the monster evolution works now: set the load position, change rooms, go back to the room you were in when it ends).