Pilot reported an Engine fuel leak during flight. A fuel imbalance developed in cruise; resulting in an in flight flame out of the Right Engine. Pilot requested diverted to make a precautionary landing.

Narrative

Aircraft XStarted with 4;390 lbs. -- End Fuel was 1;650 lbs.XA22 Engine start; XA28 Wheels Up; XC23 Generator Off R; XC24 Reset the Right Generator (IAW Checklist); XC29 Generator Off R - We left it off Left Gen load was between 65-70 Amps; XD06 Noticed a 200 lbs. fuel imbalance and transferred fuel from Left to Right; XD12 Engine Fail R; XD14 Engine Shutdown R (IAW Checklist); XD22 Landed Safely on Runway XX at ZZZI departed ZZZ1 at XA28 for ZZZ. Everything was unremarkable and standard. 2 hours into the flight at XC23 we had a Right Generator Failure. I followed the checklist and after a 'reset' it returned to 29 volts and I turned it back on. After approximately 6 minutes the Right Generator failed again. I followed the checklist a second time - but it only stayed on for a few seconds and we left it off. The checklist says if unable to restore generator land as soon as practical. I looked at the weather and determined that home was practical. Note: The temperature on this flight at altitude was the coldest I had ever seen. It was -70 degrees C. The fuel in the wings got to about -7 or -8 degrees C. As we descended into the ZZZ area (ZZZZZ arrival) I noticed that the fuel in the left tank was increasing in temperature; yet the right tank was getting colder and at one-point hit -9 Degrees C. At the time it was a curiosity. (In review the data from the G3000 I noticed that a fuel imbalance started in the decent around the way point ZZZZZ1 where the fuel difference went from a 1-6 gallon average difference for the flight and started climbing at about a gallon per min to a 30 gallon difference.) Shortly after ZZZZZ2 I felt a thud. There had been a very slight vibration in the aircraft that stopped with the thud. I would say that this occurred shortly before I noticed the 200 lb. fuel imbalance. At XD06 I noticed a 200 lb. difference and started transferring fuel from the left tank to the right. Six minutes later XD12 - around 5;000 ft. (near ZZZ2 and ZZZ3) my Right Engine failed. I was 10 minutes from ZZZ. I [requested priority handling] and followed the procedures to shut down and secure the Right Engine. My decision to [request priority handling] was based on several factors. First; I felt it would be poor form not to. We always teach to [request priority handling] if we have a problem. I also did not want to deal with vectors or altitude restrictions. I was comfortable with my location and what needed to happen next. I wanted what time I had to be able to run the checklist get ready and not have to answer much information. Essentially; I wanted an understanding with ATC that I was going to be at a high workload and needed leeway to do what I needed to expeditiously land the plane. ATC was awesome. It was a relatively straight forward single engine landing. Feet on the 1;000 ft. marks and center of the runway. After parking the plane and shutting down I went back to look at the engine. Fuel was dripping from the bottom drain area. The generator exhaust was stained brown and black. After helping the owner of the plane and his wife with their bags and got them on their way I called Company and notified them of the incident. I also removed the lower cowling of the engine. Since it was dripping fuel; I wanted to make sure that putting the plane away I was not at risk of a fire.