SF34 CREW DRAGGED ACFT WITH LOCKED BRAKES WHEN EXCESSIVE ENG PWR WAS APPLIED BEFORE BRAKE RELEASE.

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I WAS THE FO; PNF; ON A REGIONAL AIRLINE FLT FROM A MAJOR HUB ARPT IN THE SOUTHERN PART OF THE COUNTRY TO A SMALL ARPT IN THE SAME REGION ON AN SF34. UPON ARRIVING AT OUR ACFT; I PERFORMED A THOROUGH AND DETAILED PREFLT. I FOUND THE AIRPLANE TO BE IN GOOD ORDER; WITH NO DISCREPANCIES OR OPEN WRITE-UPS. THE START-UP AND TAXI WERE NORMAL AND ROUTINE. AFTER HOLDING SHORT OF ONE OF THE DEP RWYS FOR QUITE SOME TIME; WE WERE CLRED INTO POS AND HOLD BEHIND A B757 ON ITS LNDG ROLLOUT. AS WE WERE CLRED INTO POS; WE WERE INFORMED THAT THERE WAS A B777 ON A 5 MI FINAL FOR OUR RWY; AND TO BE PREPARED FOR AN IMMEDIATE DEP AS SOON AS THE B757 CLRED THE RWY. THE B757 DID NOT HURRY OFF OF THE RWY; AND THE TWR HAD TO TELL THEM TO EXPEDITE OFF BECAUSE THE B777 WAS NOW ON A 2 MI FINAL AND DOING 250 KTS OVER THE GND. WE WERE ALSO TOLD TO EXPECT AN IMMEDIATE DEP AS SOON AS THE B757 CLRED. AT THIS POINT; THE CAPT DECIDED TO PERFORM A METHOD 'A' TKOF; WHICH ENTAILS HOLDING THE BRAKES; AND APPLYING PWR TO THE ENGS BEFORE BRAKE RELEASE. AS THE CAPT BROUGHT UP THE PWR; THE ACFT SLIPPED FORWARD A LITTLE FIRST ON THE L SIDE; THEN ON THE R. I CALLED TO THE CAPT TO APPLY MORE BRAKE PRESSURE; WHICH HE DID; STOPPING THE FORWARD MOVEMENT OF THE ACFT. HE COMMENTED ON THE UNEXPECTED 'BRAKE SLIPPAGE.' WHEN THE B757 CLRED THE RWY; WE WERE CLRED BY THE TWR FOR AN IMMEDIATE TKOF. THE REST OF THE FLT TO OUR DEST WAS NORMAL. AFTER PARKING AND DEPLANING THE PAX; I PERFORMED A POSTFLT OF THE ACFT. DURING THE POSTFLT; I DISCOVERED A FLAT SPOT WITH CORD SHOWING ON THE TOP OF THE R OUTBOARD TIRE. THE FLAT SPOT WAS NOT THERE DURING THE PREFLT WHEN I INSPECTED ALL OF THE TIRES. I THEN CHKED THE OTHER 3 TIRES; AND DISCOVERED THAT THE L OUTBOARD ALSO HAD A FLAT SPOT WITH CORD SHOWING. I THEN INFORMED THE CAPT OF WHAT I FOUND. HE THEN INSPECTED THE TIRES; AND NOTIFIED OUR MAINT CTL. THEY DECIDED TO SWAP US INTO ANOTHER ACFT THAT WAS ON THE GND AT THE OUTSTATION. CONTRIBUTING FACTORS: DEP DURING A 'PUSH;' LEADING TO A TIGHT DEP WINDOW. ATC; COMPANY; AND SELF PRESSURE TO SQUEEZE INTO A TIGHT DEP SLOT; WHEN IT MIGHT HAVE BEEN BETTER TO WAIT UNTIL AFTER THE B777 LANDED.