I used to breed rats for my snakes. I just checked the feed price for the type of food I used--at $35 for a 50 lb bag, I don't see how breeding rats as chicken feed would at all be economical.
Not to mention housing. I used to have two large tower cages along with about 3 smaller cages for maternity wards and holding cages. You could also build a breeding rack for them if you want, but either way housing can be expensive/requires a bit of space. Plus bedding (although if you potty train them to a litter box the bedding lasts a lot longer), and your time for management and cleaning... Unless you just really want to raise and breed rats as a hobby (in which case they make great and very rewarding pets!), I wouldn't recommend it solely as animal feed for an animal that can get it's protein some other way.
As others have said, maybe insects?