When I am looking at the live track of aircraft in the skies over the US I see some SR20’s over Florida with the Designation of “CONN”. I suspect this is for a flight school but wasn’t sure.

I believe you are correct. We do not have registration information for the CONN callsign but most of the flight numbers I’ve looked up operate in and out of Orlando sanford (KSFB). I looked up the flight schools at KSFB and found Aerosim flight academy. They operate 75 aircraft and most if not all are Cirrus SR-20’s.

Michael 179’s deduction is correct:

In the FAA Contractions Manual (7340.2E) CONN (for “Connection”) is listed as a " Special Telephony/Call Sign for

Aerosim Flight Academy in Sanford, FL