Worth noting here is that "proton flash therapy" is a new therapy, but "proton therapy" is not. Proton therapy is a lot more recent than x-ray therapy, but still a conventional therapy.

Flash therapy is the part is which just now entering clinical trials, where you treat the patient with ultra-high dose rates (so you deliver the same dose of radiation, but in maybe 90 ms instead of 90 seconds). There are indications that healthy cells are better at recovering from the ulra-high dose rate than tumor cells are, which means it would have a protective effect on healthy tissue, but the mechanism behind it is not known. The type of radiation is not specified, it can be protons, electrons, x-rays, etc.

So "proton flash therapy" is a Flash therapy that uses protons. Other clinical trials are using electrons instead, i.e. "electron flash therapy".