"He sells (/ is selling) many different flavours of ice cream" is a bit more natural, I think. However, if you mean that the ice cream not only differs in flavour, then you could say (a) (with "with" or "of"), just don't forget an "s" on the end of "flavour".
New words, one handy idiom, and a 2-minute quiz — delivered to your inbox to keep your streak alive.