CRJ-900 Captain reported an engine flameout during climb. Flight diverted and landed safely.

Narrative

During the climb at approximately FL280 we had a R ENG FLAMEOUT warning message. There was a noticeable yaw; in addition right engine gauges indicated severe damage with diminishing rotation. We [requested priority handling] and ATC suggested diverting to ZZZ. The FO was the Pilot Flying. I ran through the QRC for Engine Fire or Severe Engine Damage in flight. We then ran ABNORMAL 1-15 for the R ENG FLAMEOUT which directed us to ABNORMAL 1-4 In flight shutdown. We communicated with the flight attendants and passengers our intention to divert. We also messaged Dispatch. We completed all of our checklists; we were vectored onto final for [Runway] XX. Visual conditions and light winds were present upon landing. We landed Flaps 20 without incident and taxied to the gate. We made an announcement to the passengers at the gate regarding the mechanical issue. The FA's (Flight Attendants) reported the passengers were calm and in good spirits. After landing we debriefed the flight; including the situation. We concluded that all went well with the exception of failing to change our transponder to XXXX. Cause: RIGHT ENGINE FLAMEOUT AND SEVERE DAMAGE.Suggestions: It is difficult to provide suggestions until a full inspection is completed on the failed engine.