It's difficult to say, and numerous factors are involved. It depends on the species you breed, the demand for them, the part of the world you are in, the local economy, and the demographic you are targeting. Not all of that is within your control. I know of breeders who made a lot of money breeding softbills. They had rare species that brought in the high dollars, and common species that paid for the supplies. It was their life, not just a hobby on the side. They didn't just buy some birds and start making money. It began small and gradually expanded over the years.
If you're talking about parrots, then you must consider the initial investment, the time you're willing to devote to it, and the ongoing expenses. There may be local or national laws that restrict the species you have access to. Most breeders will tell you that they either lose money, barely break even, or make a minimal profit. There were years when we made good money, and there were very bad years that hurt our savings. Financially, over the years, I would say we broke even.
Are you going to get rich from it? No, not unless you find a rare species that's in high demand and you have the financial means to get started. It can be both rewarding and heartbreaking. If you're willing to put the work in, the love you get in return is worth it. Love will fill your heart and soul, but unfortunately, it won't pay the mortgage.