There are only about a dozen combinations that will produce that fish, and the silky fin is one that can't be obtained by breeding totally different fin types, so you'll need at least one silky-finned fishie to make the silky beta. The silky fin can come from two silky finned parents, or one silky and one tiger. To get a beta you can breed either a carp or leaffish with a banafish. So, for example, you could breed either a silky or tiger carp with a silky bananafish to get the silky beta.

You can find other combinations by checking out the spoilers post in the Fish Tycoon Guide!