A Certified Flight Instructor (CFI) was flying with an Airline Transport Pilot (ATP) rated pilot. The ATP pilot asked the CFI to assist the ATP pilot with an Instrument Proficiency Check and a Flight Review pursuant to 14 CFR 61.56 (a). The ATP and CFI were flying a Cessna 210, called N549KS. While climbing out from Akron Canton Airport (CAK), Air Traffic Control (ATC) directed the N549KS to turn to heading to 360 and climb to 4000. Somehow, the autopilot jammed and the ATP was flying the aircraft climbed to 8000 feet almost causing a collision with an inbound jet descending. ATC told N549KS to call a local phone number upon landing and nothing else. The flight continued without further incident.