DC10 FLT CREW EXPERIENCED NMAC DURING VISUAL APCH INTO AFW WHEN SEQUENCED BEHIND T38 ACFT NOT IN SIGHT; BOTH ACFT EXECUTED EVASIVE ACTION.

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FLT ARRIVING AT AFW ARPT WAS BEING VECTORED TO FINAL APCH FOR RWY 16L FROM THE W. THE FO WAS THE PF. APCH CTL TOLD US THAT WE WERE #3 BEHIND A COMPANY ACFT. WE HAD HEARD THE ACFT WAS TO FOLLOW A C5. ABOUT 10 MI ON FINAL WE WERE HANDED OFF TO AFW TWR. THE TWR TOLD US WE WERE #3 FOLLOWING A T-38 ON A L-HAND DOWNWIND. THE CAPT IMMEDIATELY SAID WE DID NOT HAVE THE TFC. THE CAPT AND MYSELF LOOKED FOR THE TFC WHILE THE FO CONTINUED THE APCH. WITHIN 20 SECONDS; I SAW THE T38 AT OUR 10 O'CLOCK POS AT LESS THAN 1 MI. WE GOT A TA AND THE CAPT SAID 'LET'S GO AROUND.' WITHIN A FEW SECONDS LATER; WE GOT AN RA AND RESPONDED INTO STEEP CLB INDICATED BY OUR VSI. THE T38 (WHICH WE NEVER HEARD ON TWR FREQ) WENT INTO A DIVING R TURN AND WENT DIRECTLY UNDERNEATH US. THE CAPT LEVELED OFF THE CLB AT 3500 FT AND MADE SURE THE FO WAS THE PF. THE TWR SAID WE WERE CLR TO LAND; BUT WE DECLINED; BEING COMPLETELY OUT OF POS FOR A STABILIZED APCH. THE TWR GAVE US A L TURN TO A DOWNWIND POS AND SAID SQUAWK 1200...UNABLE FOR US. THE TWR TOLD US WE WOULD BE #1 IN FRONT OF ANOTHER C5 ON FINAL. THE CAPT DECLINED THE VISUAL APCH (FLT VISIBILITY WAS MVFR). WE RETURNED TO APCH CTL AND GOT VECTORED TO A REASONABLE APCH AND LNDG.