MLG HAS SMOKE FROM L GEAR ON LNDG. 2 FLAT TIRES.

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THE FLT BTWN SLC AND MCI SEEMED UNEVENTFUL UNTIL FINAL APCH AT MCI. NONE OF THE 5 CREW MEMBERS HEARD OR FELT ANYTHING UNUSUAL DURING THE TKOF AT SLC; CLB AND CRUISE; OR DURING THE LNDG AND ROLLOUT AT MCI. THE ONLY UNUSUAL OCCURRENCE WAS THAT L MAIN GEAR DID NOT INDICATE GREEN ON INITIAL EXTENSION. IT WAS CYCLED ONCE AND ALL INDICATIONS WERE NOW NORMAL. A NORMAL LNDG WAS MADE ON 19L AND A TURNOFF AT THE LAST HIGHSPD. AS WE APCHED THE RAMP IT BEGAN TO FEEL LIKE A ROUGH TXWY AND ANOTHER ACFT RPTED SMOKE FROM OUR L GEAR. TWR INSPECTION RPTED NO FIRE. MAINT INSPECTION REVEALED THAT BOTH TIRES WERE NOW FLAT AND THE ENTIRE CAP ON THE OUTBOARD TIRE WAS GONE ALONG WITH HALF OF THE GEAR DOOR; AND THE SIDEWALL WAS SHREDDED BY THE WHEEL. THE INBOARD TIRE WAS SCORED DOWN THE MIDDLE AND THE OUTBOARD HALF OF THE CAP WAS MISSING. LITTLE OF THE DEBRIS WAS FOUND ON THE RWY AT MCI AND IT WAS LATER TOLD TO US THAT MUCH DEBRIS WAS FOUND AT SLC. IT SEEMS THAT AN ACFT RPTED DEBRIS TO SLC TWR. IT WAS PICKED UP AND DETERMINED TO BE MLG PARTS. THE TWR THEN COULDN'T IDENT WHO RPTED THE DEBRIS SO THE COMPANY HAD TO DEDUCE WHO IT WAS. THEY ERRONEOUSLY DEDUCED THAT IT WAS OUR FLT THAT MADE THE RPT AND NOTIFIED A POSSIBLE HAZARD TO 3 OTHER ACFT WHO DEPARTED BEFORE US. WE WERE NEVER CONTACTED TO CONFIRM THE DEDUCTION. FORTUNATELY; AT LEAST 1 TIRE WAS INFLATED FOR OUR LNDG; ALLOWING FOR A SUCCESSFUL ROLLOUT; BUT IF BOTH HAD BEEN FLAT; THE RESULTS NO DOUBT WOULD HAVE BEEN VERY DIFFERENT. THE INTERACTION BTWN THE ATC TWR AND COMPANY WAS VERY UNSATISFACTORY; AND PREVENTED ME FROM HAVING CRASH EQUIP STANDING BY FOR OUR SAFETY.