Beech 1900 Captain reported Trailing Edge Flaps stuck in takeoff position during approach. The flight crew performed a go-around and ran the check lists and QRH. The flight crew then continued to land at destination airport with the flaps remaining in takeoff position.

Narrative

On visual approach into ZZZ; when I was on the left downwind abeam the numbers for Runway XX; I tried extending approach flaps before extending my landing gear only to find out my flaps were stuck in the takeoff setting. I attempted to trouble shoot while continuing to turn left base for Runway XX. I noticed no popped circuit breakers and I was unable to even retract flaps to fully up position; so I requested a go-around with tower. Tower asked if I'd stay with them or go back to terminal I said I'd stay with tower and in the traffic pattern VFR to run numbers to prepare for a no-flaps landing. I maintained 2;000 feet as requested by Tower to stay in right close traffic while running numbers I needed for a no flaps landing. Approximately 5 minutes later; I landed at ZZZ safely with flaps stuck in the takeoff position. Have to prepare for a potential no flaps landing. But after realizing the flaps were stuck in takeoff position without being able to retract it to fully up position; I made the PIC decision to land using the no flaps landing data I calculated from the POH since that data is more restrictive.