A POTENTIAL CONFLICT ENSUES WHEN A MIL T38 ACFT HAS A FLAMEOUT AND DSNDS INTO B737-300 TFC HELD BELOW AS OPPOSITE DIRECTION TFC AT FL230; ON FREQ WITH ZLA; CA.

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I WAS THE PF. WE WERE CLRED TO FL230 AND TOLD THAT WE WERE RESTR TO THAT ALT FOR OPPOSITE DIRECTION J-38 TFC AT FL240. I HAD JUST LEVELED OFF AT FL230 AS WE GOT VISUAL CONTACT WITH THE T38. JUST MOMENTS LATER; IT SEEMED THAT THE T38 WAS DSNDING TOWARD US; FOLLOWED BY A 'TFC' TCASII ALERT. WITHIN SECONDS; WE HAD A 'DSCNT' RA. I IMMEDIATELY DISCONNECTED THE AUTOPLT AND DSNDED AT A RATE IN EXCESS OF 2000 FPM; FOLLOWING THE VSI TCASII ADVISORY. MY CAPT MADE A DEV CALL TO ZLA AND KEPT HIS EYES CLOSELY ON THE TFC. HE FELT THAT THE T38 WAS NOW BANKING TOWARD US AND ANNOUNCED 'MY ACFT' TAKING THE CTLS AND BANKING TO THE L; AWAY FROM THE T38. AT THAT POINT; THE T38 DSNDED THROUGH OUR ALT AS WE HAD A 'DSND' AND 'CLB NOW' ADVISORY ALMOST INSTANTLY. I HAD NOT SEEN THE ACFT BANKING TOWARD US AND IT IS DIFFICULT FOR ME TO JUDGE THE DISTANCE. ZLA ADVISED US LATER THAT THE T38 PLT HAD JUST EXPERIENCED AN ENG FAILURE WHICH PROMPTED HIM TO INITIATE A DSCNT. AT THE TIME OF OUR DEV; WE WERE NOT AWARE OF THE T38 EMER STATUS. SUPPLEMENTAL INFO FROM ACN 563456: WE WERE LEVEL AT AN INTERMEDIATE LEVELOFF. ATC TOLD US WE WOULD BE THERE FOR 4 OR 5 MINS DUE TO TFC. ATC CALLED OUT TFC AT 11 O'CLOCK POS; A T-38; FL240. WE VISUALLY ACQUIRED RIGHT AWAY. A XCHK OF THE TCASII SHOWED HIM 300 FT LOW. ONCE THE INCIDENT WAS OVER; ATC DID INFORM US THE T38 HAD RELAYED TO THEM THAT THE ACFT WAS AN EMER DUE TO A FLAMEOUT. THEY ALSO INFORMED US 'THE 2 TARGETS WERE LESS THAN A MI (APART).' THE MANEUVERING WAS ENOUGH THAT THE CABIN CREW CALLED TO SEE WHAT WAS GOING ON; BUT NOT ENOUGH TO CAUSE ANY TYPE OF CABIN UPSET.