These two things are inconsistent. Kansas City, Kansas is on the northern side of "town."
In any event, there are a few different options around town:
1) ATD at the Kansas City Downtown Airport (KMKC) -
http://atdflightsystems.com/
2) McCullough Aviation at Kansas City Downtown -
http://www.mcculloughaviation.com/
3) Air Associates at Johnson County Executive (KOJC) (nice big fleet, but probably the most expensive option in town)-
http://www.airassociatesinc.com/
4) New Century Air Service at New Century airport (KIXD) (one of the least expensive options) -
http://newcenturyairservice.com/
5) There was a flight school at the Gardner, Kansas airport (K34), but I'm not sure it's still operating. If it is, there's no website.