What flux should I use for copper that will be used for food prep?
All the flux is for is to make the solder wick around the copper more easily to give you a better join.

As long as you're using lead free flux, after you complete the solder joins, run the water for several minutes from each fixture and you're not going to have any worries.  People have been using flux w/ copper for decades now w/o any harmful side effects.