AN A320 CREW RPTS A NEAR MISS WITH AN FAA FLT CHK ACFT APCHING DEN.

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THE INCIDENT OCCURRED AT APPROX XA30 LCL IN DENVER. IT WAS VFR; WINDS WERE 170 DEGS/10 KTS AND DENVER WAS LNDG RWYS 17R AND 16L. TFC LNDG RWY 16L WERE EXPECTED TO CLR AT END DUE TO CONSTRUCTION ON ALL HIGH SPD TXWYS. UPON BEING HANDED OVER TO APCH CTL WE WERE TOLD TO EXPECT A VISUAL TO RWY 16L. SOON AFTER WE HEARD A CONVERSATION BTWN A FLT CHK XX AND DENVER APCH. FLT CHK XX SAID HE WANTED TO DO SOME ARCING TYPE MANEUVERS N OF DEN IN THE AREA OF RWYS 17L/R. FLT CHK XX WAS WARNED ABOUT ARRIVING TFC BUT WAS SUBSEQUENTLY CLRED TO DO HIS MANEUVERING. WE WERE ON A R DOWNWIND AND EVENTUALLY GIVEN A CLRNC TO 8000 FT. AT SOME POINT ON THE DOWNWIND I HAD DISCONNECTED THE AUTOPLT AND AUTOTHROTTLES. APCHING ABEAM LEETS APCH ASKED US IF WE HAD COMPANY AIRBUS AT OUR 3 O'CLOCK POS. WE ACKNOWLEDGED HAVING THEM IN SIGHT AND WERE CLRED TO FOLLOW TFC; CLRED VISUAL TO RWY 16L. I TURNED TOWARDS LEETS AND HAD MY FO SET 7000 FT AND I STARTED TO SLOW TO 180 KTS FROM 210 KTS. APCHING LEETS I CALLED FOR GEAR DOWN FINAL DSCNT CHKLIST AND I BELIEVE MANAGED SPD. AT ABOUT THIS TIME APCH CALLS OUT TFC TO US OFF TO OUR 10 O'CLOCK POS. I SENSED A LITTLE ANXIETY IN HIS VOICE. WE DIDN'T ACKNOWLEDGE HIS FIRST CALL BUT ACKNOWLEDGED HIS SECOND. I BELIEVE WE DIDN'T ACKNOWLEDGE HIS FIRST CALL BECAUSE WE WERE VERY BUSY GETTING CONFIGURED AND WATCHING THE AIRBUS TFC IN FRONT OF US. I PICKED UP THE TFC AND HE TOLD ME NOT TO DSND BELOW HIS ALT. BEFORE I COULD REACT WE GOT A TCAS RA WHICH CALLED FOR AN AGGRESSIVE CLB OF ABOUT 1500/2000 FPM. I ACCOMPLISHED THE MANEUVER AND WHICH LASTED ONLY A FEW SECONDS. ONCE CLR OF TFC I CONTINUED MY DSCNT TO RWY 16L. I WAS ABLE TO GET THE AIRPLANE RE-STABILIZED ACCORDING TO ACR X SOP GUIDELINES AND LANDED WITHOUT INCIDENT. TALKED TO MR X OF DEN APCH AND WAS TOLD OUR VERT SEPARATION WAS 200 FT. HE TOLD ME FLT CHK XX WAS VFR; HAD ME IN SIGHT AND WAS TOLD TO MAINTAIN VISUAL SEPARATION FROM ME. IT WAS WHEN OUR PATHS WERE CONVERGING AND FLT CHK XX MAINTAINING 6900 FT THAT PROMPTED DEN TO CALL US.