A321 Captain experiences locked flaps on departure. A flap indicator circuit breaker reset allows the flaps to be retracted normally. On descent the left engine ceases to respond to throttle movements and the flap problem reappears. This results in a partial flap single engine landing at a diversion airport.

Narrative

The flight departed normally but on initial flap retraction (from flaps 1 to up) we received an ECAM stating that the flaps were locked. With no roll tendencies I felt that it was an indicator problem and not an actual flap problem. I reset the flap indicator CB and the ECAM cleared and the flaps retracted normally without any further problems noted. This indicated to me that the issue was indeed in the indication. The rest of the flight until the descent went normally. On initial descent out of FL380; with the autothrust engaged; the engines came back to idle as commanded for the descent. Once the engines were at idle we began to receive various ECAM items indicating that engine 1 (left engine) has a malfunction and was thus unable to produce thrust although it was still running at idle. Throttle movements had no effect on the engine. The right engine was still operating normally. I took over flying duties from the First Officer and instructed him to declare an emergency with Center and changed our destination (due to our planned destination having no instrument approach and a short runway). We were handed off to Approach Control. Shortly thereafter we began to receive another series of ECAM messages indicating possible flap issues. At this point I instructed the First Officer to get clearance for the longest runway at ZZZ. He suggested having the emergency equipment standing by. We finished the ECAM procedures as directed. On flap extension the flaps locked at slats 3 and flaps less than 1. We added the appropriate speed corrections IAW the flight manual and made an uneventful landing. In retrospect the flap issue on departure may have not been an indication issue but a sensor issue. The flap problem when combined with the engine failure; although not related to each other; made for a compound emergency.