SR22 pilot reported engine roughness during cruise for a post-maintenance ferry flight. The pilot diverted to another airport where the engine shut down on its own after landing and exiting the runway.

Narrative

Aircraft was being transported from maintenance facility [at] Company A; located at ZZZ; following a major engine overhaul. Engine overhauled by Company B. Aircraft had been previously ground tested to manufacturer instructions; and maintenance facility pilot had performed 1 hour test flight earlier in the day. The aircraft was filled to the top with fuel significantly more than needed for flight. I properly preflighted aircraft; including taking fuel samples from all fuel sample locations; which were free of contaminants; and checked oil. Prior to departure; conducted proper ground run-up and noted no anomalies.I departed ZZZ at XA:13. During the first approximate 47 minutes of flight; following departure of ZZZ for ZZZ1; engine performed as expected as I closely monitored all engine parameters using both engine monitor and gauges. Abruptly; the fuel flow gauge dropped from 20 GPH to 0; but 20 GPH was noted on the separate engine monitor page of the Cirrus MFD (Multi-function Flight Display). I immediately turned on the auxiliary fuel pump; adjusted mixture to full rich; and switched tanks. The fuel flow gauge resolved to 24 GPH and was confirmed by the engine monitor fuel flow display. After a few seconds of normal indication; the fuel flow gauge dropped again to 0; then began randomly oscillating between 0 - 20 GPH. The significant drop in fuel flow was noted on the engine monitor. I cycled the boost pump and switched tanks again; but the drop in fuel flow remained with the gauge showing 0 GPH. I noted a roughness developed in the engine; observed ZZZ2 at my 1 o'clock and; fearing an imminent loss of power; [requested priority handling] with the Center Controller. I executed an immediate descent from 7;500 ft. as the runway appeared within gliding distance. I noted a further roughness in the engine develop during the descent. The controller provided me with CTAF frequency and I announced I was attempting a landing on Runway XX. I successfully executed the landing; announced on Center frequency that I was safely on the ground. I safely exited the runway... at which point the engine shut down by itself despite a full rich mixture setting and auxiliary boost pump on. At time of shutdown the aircraft had approximately 60 gallons of fuel onboard. Maintenance personnel towed the aircraft to a tiedown and it is awaiting further inspection.