A KING AIR FLT CREW DETECTED AFTER LNDG THAT THE 2 OUTBOARD TIRES HAD DEFLATED ON LNDG.

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I WAS THE PIC AND THE PF FROM THE R SEAT OF A KING AIR BE-B200 DURING LNDG AT WEST CHESTER (BRANDYWINE; N99); PA. THE WX WAS SLIGHTLY ABOVE VOR MINIMUMS SO WE DECIDED TO FLY A VOR APCH TO THE RWY. (THERE IS NO LOC AVAILABLE.) WE ACQUIRED THE RWY ENVIRONMENT AND TRANSITIONED TO VISUAL REFS FOR THE LNDG. WE LANDED SLIGHTLY LONG AND SLIGHTLY FAST; BUT NOT SO LONG OR FAST AS TO BE CONCERNED. WE BROUGHT THE ACFT TO TAXI SPD USING ORDINARY PROCS; TAXIED TO PARKING AND SHUT DOWN. UPON OUR POSTFLT VISUAL INSPECTION; WE NOTICED THE MAIN GEAR TIRES APPEARED TO BE FLAT. (THERE ARE 2 WHEELS ON EACH MAIN LNDG GEAR.) UPON CLOSER INSPECTION; BOTH OUTBOARD TIRES WERE FLAT-SPOTTED AND DEFLATED; WHILE BOTH INBOARD TIRES WERE STILL INFLATED. THERE WAS NO OTHER DAMAGE TO THE ACFT. WE CALLED MAINT AND THEY DISPATCHED A MAINT CREW TO INSPECT AND REPLACE THE TIRES. THE MAINT CREW CONFIRMED THE INBOARD TIRES WERE STILL INFLATED AND OK; BUT THE OUTBOARD TIRES NEEDED TO BE CHANGED. THEY DID SO AND RELEASED THE ACFT TO FLY. IN TRYING TO UNDERSTAND WHY THE 2 OUTBOARD TIRES HAD BEEN FLAT-SPOTTED; I BELIEVE THEY WERE SOMEHOW SUBJECT TO MORE BRAKING FORCES THAN THE INBOARD TIRES WERE. I CAN ONLY BELIEVE THAT PERHAPS I 'JUMPED ON' THE BRAKES TOO HARD INITIALLY; BECAUSE THERE WAS NOTHING UNUSUAL ABOUT THE REMAINDER OF THE RWY ROLLOUT AFTER LNDG; AND WE SLOWED TO TAXI SPD WITH APPROX 1000 FT OF RWY REMAINING. WE DID NOT FEEL OR HEAR ANYTHING DURING THE ROLLOUT OR TAXI TO PARKING. I'M GLAD A POSTFLT VISUAL INSPECTION IS IN MY HABIT PATTERN.