I was wondering if I could pass down multiple eggs moves in Pokemon Insurgence, because I am breeding a Lopunny and I was wondering if it could have Ice Punch and Fake Out. If you could help me, it would be greatly appreciated! 
Yes, multiple egg moves can be bred, it works like the core games. No pokemon has both ice punch and fake-out though, so you would have to breed fake out with say, a Makuhita, and then breed the baby with fake-out with a Medicham to get ice punch and fake out on It’s baby. Makuhita and Medicham are just examples, other pokemon work, for a list of what pokemon will work use http://pokemondb.net/pokedex/lopunny/egg.
Oh, thanks Unique!
Or you could get a smeargle with those moves and breed it.
Thank you Cow358 
You are welcome.
The easiest way that I found is to get a tyrogue that knows fake out, evolve it into hitmonchan and teach it ice punch, then breed it with a female buneary line.
That too. If you do what @megastone suggested you can also get Fire Punch and Thunder Punch