when my sump pump in the basement runs, the kitchen drain gurgles
It sounds like a venting issue to me. Did you vent specifically the fitting into which the sump pump dumps? Without a vent for itself the pump dump water is going to suck air from somewhere.  Also, now in our area all basement type pumps have to be dumped into a vertical line.  And I believe that vertical line has to be at least one pipe size larger then previously required.  P.