Should I flush my sump pit with water?
Approximately never.

If you notice things growing in there or bugs breeding, a bit of soap (liquid dish detergent would be my first choice) will usually do in the bugs by altering the surface tension, and chlorine bleach will kill off bacterial slimes if there's not too much water flow (so it stays put for a while.) If there is water flow it should never get too nasty.

If you are not experiencing problems/smells, leave it alone - or perhaps put a cover over it if it lacks one, which will keep things from going into it and causing problems (small animals drowning, for instance - or the bugs that might want to breed in there.) If it also serves as a floor drain, put a screened section in the cover to allow water to flow in.