ACFT EQUIP PROB. DUAL ENG FLAMEOUT. CAUSE UNK; BUT PROBABLE ICING PLUS TURB CONTRIBUTED. AFTER R ENG FLAMED OUT; IGNITERS WERE TURNED ON. WHEN THE L ENG STARTED TO FLAME OUT; APPEARED TO HAVE SEVERAL COMPRESSOR STALLS PRIOR TO THE FLAMEOUT. AT LOWER ALT; ENGS WERE RELIGHTED AND FLT CONTINUED NORMALLY.

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FLYING A LEAR 25 FROM WILLOW RUN; MI; TO DALLAS LOVE; TX; ON A 4 PAX CHARTER FLT AT FL390 OVER A WIDESPREAD TSTM/IMC AREA EXPERIENCING INTERMITTENT LIGHT TO MODERATE TURB; I DECIDED TO CLB TO FL410 TO TOP THE RISING WX AND GET OUT OF THE TURB WHILE ALSO BEING MORE FUEL CONSERVATIVE. CLBING THROUGH FL400 THE R ENG FLAMED OUT. ENG SHUTDOWN AND DSCNT PROCS WERE INITIATED WHILE NOTIFYING ATC OF OUR SIT. THE IGNITERS WERE ALSO TURNED ON. DURING THE DSCNT PASSING THROUGH APPROX FL385 THE L ENG ALSO FLAMED OUT; LEAVING US WITH NO PWR OR PRESSURIZATION. AN EMER DSCNT WAS INITIATED AND PAX OXYGEN MASKS WERE DEPLOYED WHILE ATC WAS NOTIFIED OF OUR EMER DSCNT TO A MAX OF FL250 TO RELIGHT THE ENGS. WE SQUAWKED 7700. ATC TOLD US TO MAINTAIN FL350 AND WE TOLD THEM WE WERE UNABLE. APPARENTLY WE WERE DSNDING THROUGH A HOLDING PATTERN WITH A STACK OF AIRPLANES IN THE PATTERN. AT FL250 RELIGHT PROCS WERE PERFORMED AND BOTH ENGS WERE RESTARTED BY FL230 WHERE WE LEVELED OFF. WE REQUESTED AND RECEIVED A CLB CLRNC BACK TO FL350. WE CLBED TO FL350 (AND LATER TO FL370) TO TOP THE WX AND CONTINUED ENRTE TO DALLAS LOVE FIELD. THE CREW AND PAX WERE UNHARMED DURING THE EVENT. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR CAPT DID NOT KNOW WHAT CAUSED THE ENG FLAMEOUTS. WHEN THE FIRST ENG (R) FLAMED OUT; THE RPTR CONTACTED ATC SAYING; 'WE'RE IN AN EMER DSCNT AND SQUAWKING 7700.' RPTR SAYS THAT THE CTLR WAS ON A LANDLINE AT THE TIME OF HIS CALL AND APPARENTLY DIDN'T REALIZE THE SERIOUSNESS OF HIS SIT. PLUS; THE CTLR WAS WORKING MANY ACFT WHICH WERE IN A HOLDING PATTERN BENEATH THE RPTR ACFT. AN EMER WAS NOT DECLARED BY THE FLC. THE CTLR; SEEING THE ACFT DSNDING DOWN THROUGH THE HOLDING PATTERN BECAME VERY BUSY SCRAMBLING ACFT OUT OF HIS WAY. WHEN THE ATC CTLR REQUESTED; 'CAN YOU TAKE A TURN?' THE RPTR ANSWERED; 'NEGATIVE.' RPTR'S RESPONSE TO WHY HE WOULD NOT ACCEPT A TURN WAS THAT HE WAS VERY BUSY AT THE TIME AND COULDN'T BE DISTR BY TURNING TO A VECTOR HDG. CONSEQUENTLY; RPTR ACFT DSNDED DOWN THROUGH A HOLDING PATTERN UNTIL FL250 WHERE THE FLC WERE ABLE TO RELIGHT BOTH ENGS.