CRJ-700 Captain reported during descent that the number 2 engine flamed out and relighted after ten seconds. Flight continued to destination.

Narrative

We were at FL 310 descending down to 11;000 and suddenly we had a R eng flame out. I had added some left rudder pressure to counteract the yaw. As we were about to run QRH; right engine re-lighted after we lost our engine for about 10 seconds. We still ran QRH and it said; that we don't have to do anything if engines relighted. Shortly after that; we had a L/R FADEC (Full Authority Digital Electronic Control) fault status messages populate on our ED2 (Engine Display 2). We ran the QRH and there was no procedure. We were told to descend to 4;000; but I told the controllers that we need to stay at 9;000 and we need delayed vectors. I had told them we lost our right engine; but it relighted. I gave the plane to my FO and I contacted dispatch/maintenance through ARINC on XXX.XX. As I was talking to them; the FADEC fault status messages went away. I didn't feel comfortable flying into ZZZ because we were headed for XX and if we did have another flame out then; we wouldn't have the climb gradient to out climb the mountains. I thought about turning on continuous ignition for the approach; but I wanted to follow procedures/checklist and not do anything out of the ordinary. We had about 3.2-3.5 FOB and I knew that we were low on fuel so I needed to make a decision in a timely fashion. Dispatch and I made a joint decision to land in ZZZ only because the posted messages went away. Throughout the whole approach those EICAS messages we got were out of view on ED1 (Engine Display 1)/ED2 We landed and after we had landed; the L/R FADEC fault status messages came back into view along with APR CMD SET caution message and rudder limiter fault status messages immediately came back in to view. All I knew was that I needed to work at a timely fashion and make sure everything was squared away and that my FO was feeling comfortable with commencing the approach as well. I told my FO to keep me honest if he didn't like anything in terms of speed; altitude or glide path angle then call a go around. But thankfully we were able to land the plane safely. Suggestions: The mic transmit button on CA side on Yoke was INOP and the RT/IC switch doesn't work that well captain side pedestal. Please check it and fix it.