Hello, Gwen, I'm fairly new to whistles, my cleaning so far has been of pre used instruments, but I would think not very often, unless you are a wet blower.
None of mine have any indication of needing cleaning yet, nothing in the barrel or fipple. If you do see any build up, that would be the time to give them a clean.
I don't think small amounts of deposit would affect the quality of sound much, but it's nice to keep them looking good anyway.