Here is a previous thread with more information on the subject.
There is some discussion on the use of F# designation. It is often used to note distance from wild caught fish in pure species. It is also used to document hybrids or crosses between varieties of all sorts of plants and animals.
I assumed (perhaps incorrectly) that with flowerhorns, folks were using f1, f2 and so on to refer to crosses between a flowerhorn and a vieja, not necessarily keeping within the same exact family.
Here is a link to a FB post with more information, using the term to discuss breeding within a family and not introducing any new genetic material besides the initial mother and father. That is difficult due to the fertility problems with many vieja and parrot crosses.
It's a bit confusing to keep track of because the modern flowerhorns are dozens of generations down from the initial crosses of trimaculatum and parrots, herichthys, and who knows what else. But if you take the crossbred flowerhorn and breed it with a pure vieja or a parrot, the term is f1 kamfa.
I don't know if any breeders of flowerhorns that are working past, say, F4 without adding any new genetic material, and frankly, I don't think I would want one that was that inbred. When you get past even f3, unless you are only working with the original two parents' genetics, I don't see the point of labeling it f4, f5, f6 etc because they've just joined the mishmash of genes that make up the flowerhorn anyway.