The dilemma is that you don't want an already sick fish to starve, notwithstanding that the best way to get a cichlid to eat what you want it to eat is to deny it anything else.
That said, HITH/hexamita call it what you may is a) very quickly reversible and in pristine water would take a good old long time to become permanently disfiguring/fatal and b) does not usually, especially in the early stages, weaken a fish much.
I think your best course of action is to deny it any bloodworms whatsoever while maintaining a strict regime of daily large water changes. Hopefully within a couple of weeks it will be taking other foods. A good cichlid pellet would be great - personally I really like NLS Cichlid Formula, and your other fish will be good on that as well which makes it especially nice - together with some spirulina supplement, pellet or flake. Blanched veggies can go down nicely too but it can take longer to get them eating these.
Not sure what flake you're using - but look for something high quality which indicates it is designed for cichlids. Again, New Life Spectrum is very good all round.