BE33 HAS CLOSE ENCOUNTER WITH BE90 LANDING OPPOSITE DIRECTION ON SAME RWY AT FLG.

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AFTER MAKING AN INTERMEDIATE LNDG AT INW; WE CONTINUED TO FLG. WE MADE A VISUAL APCH TO THE ARPT; WHICH HAD RWY 3 IN USE DUE TO WIND. ON THE FIRST APCH TO A LNDG; WE ENCOUNTERED WIND GUSTS AND MADE A GAR. THE TWR TOLD US TO MAKE L-HAND TFC TO RWY 3 AND WE CONTINUED IN THE VFR TFC PATTERN FOR A FULL STOP LNDG. THE LNDG WAS GOOD WITH A TOUCHDOWN ZONE LNDG. AS WE ROLLED OUT; WE NOTICED A BEECHCRAFT KING AIR C90 COMING DIRECTLY AT US ON RWY 21. THE TWR WAS UNAWARE OF THE LOCATION OF THIS ACFT UNTIL HE WAS OVER THE THRESHOLD OF RWY 21. WE EXPEDITED THE TURNOFF ON A TXWY TO AVOID THE OTHER ACFT. AS WE WERE EXITING THE RWY; THE KING AIR MADE A GAR FROM A VERY LOW ALT. THE TWR ASKED THE PLT OF THE KING AIR IF HE KNEW WHAT THE ACTIVE RWY WAS. THE CTLR THEN TOLD THE KING AIR TO RE-ENTER THE BASE LEG FOR RWY 3; WHICH WAS DONE WITH AN OVERSHOOT ON FINAL. AFTER LNDG; I TALKED TO THE PLT OF THE KING AIR; WHO SAID THAT HE WAS UNAWARE OF TFC ON RWY 3. THE TWR REQUESTED A PHONE CALL FROM HIM; AND I LATER FOUND OUT THAT THE TWR REQUESTED A 7 MI FINAL CALL AT SHUTE INTXN ON THE ILS RWY 21 APCH TO FLG. THE KING AIR PLT DIDN'T MAKE THIS CALL AND CONTINUED HIS STRAIGHT-IN APCH TO RWY 21; UNAWARE OF TFC ON RWY 3. THE TWR CTLR DIDN'T REALIZE THE POS OF THE KING AIR UNTIL HE WAS ON SHORT FINAL TO RWY 21. BECAUSE OF OUR QUICK RESPONSE TO CLR THE RWY; WE AVOIDED WHAT COULD HAVE BEEN A COLLISION OF 2 ACFT ON THE RWY. THE TWR AT FLG ENTERED A 'PLTDEV' TO THE FAA FOR THE KING AIR CREW BECAUSE OF THE LACK OF AWARENESS IN CLASS D AIRSPACE AND THE LACK OF REQUIRED RADIO COMS.