STUDENT PLT; WITH INSTRUCTOR; BLEW A MAIN TIRE ON A SMALL SINGLE ENG LOW WING ACFT AFTER LNDG ROLL. HVY BRAKING WAS USED TO TURN OFF RWY SHORT FOR LNDG TFC.

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LANDED RWY 6 AT ROA WITH STUDENT PLT; NORMAL LNDG AND ROLLOUT. SEVERAL OTHER TOUCH AND GO ACFT IN PATTERN WITH ONE ON FINAL. TWR DIRECTED ACFT TO 'CLR RWY 6 AT TXWY L' WHICH WAS VERY CLOSE. BEGAN BRAKING SOMEWHAT HARD TO MAKE TXWY L WHILE BRIEFING STUDENT ABOUT EXCESS BRAKING; TURNING SPDS AND SIDE LOADS. REALIZING IT WOULD BE CLOSE; I CONSIDERED NOT ACCEPTING TXWY L WITH ADVISING THEM OF 'UNABLE.' HOWEVER; CONTINUED TO BRAKE FOR TXWY L AND MADE IT AND STOPPED IN SAFE AREA SHORT OF HOLD LINE. GND CTL INSTRUCTED 'HOLD SHORT TXWY G; TFC.' HELD POS ABOUT 1-2 MINS; WHILE JET TAXIED BY. THEN HEARD 'POP' AND TIRE BLEW. EVENTUALLY; WITH TAXI CLRNC; TAXIED TO RAMP WITH BLOWN TIRE. I FAILED TO EXERCISE PIC AUTH TO NOT ACCEPT ATC INSTRUCTION WHICH WAS UNSAFE FOR MY FLT. OVER-BRAKING RESULTED IN LOCKED BRAKE (OF WHICH I WASN'T AWARE); FLAT SPOT AND EVENTUAL BLOWN TIRE; RESULTING IN DISABLED ACFT BTWN ACTIVE RWY AND TXWY. I WILL BETTER ASSESS THE SAFETY OF FOLLOWING ATC INSTRUCTION IF I HAVE ANY CONCERN ABOUT THE SUCCESSFUL AND SAFE OUTCOME IN THE FUTURE.