Just caught up to this thread tonight. I had posted a seperate thread in the General section a few days ago. I was on the same ATC frequency as the Beechjet that reported the problem. We were in a Lear 60 at FL400 in southern Virginia and talking to Center.
Center was very busy with air traffic and the Beechjet broke into the frequency with a quick "Mayday, Mayday" or "Break, Break" (can't remember the exact phrase used, but it was urgent). They then stated, "Beechjet N???? declaring emergency, dual engine flameout." Center asked for a confirmation of the emergnecy. Beechjet responded, "Affirmative, declaring an emergency, both engines have failed, unable to maintain altitude and request vectors to the nearest airport." Center responded with a vector towards Norfolk (ORF). They were then cleared to a lower altitude. Each transmission from the pilots' voices indicated a very high stress level. In fact, I have never quite heard that panic sound in any pilots voice. I imagine they were very busy navigating to ORF and trying to relight.
In any case, we got a frequency change and attempted to monitor this situation with the other radio. However, we quickly got out of range and last I heard, they were through FL240 with no relight yet, still getting vectored to ORF. Through hearsay, I heard they got one relit and that they landed safely. Lack of news reports probably confirms that.
Also hearsay....I understood the problem to be a poor mixture of prist in the fuel. Who knows? Well, that is my story and I'm sticking to it!