B737 FLT CREW ENCOUNTERS TRW ON ILS APPROACH COURSE ABOVE 3000 FT AGL AND FO ANNOUNCES INTENT TO GAR. CAPT ASSUMES CONTROL AND LANDS AFTER SEVERAL FLAP OVER-SPEEDS. LANDING CHECKLIST IS NOT COMPLETED.

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INBOUND TO ZZZ; LARGE TSTM CELLS DEVELOPING OVER THE FIELD. FLAPS 5 DEGS AND 4000 FT ON THE BASE TURN; I MENTION MY CONCERN OVER THE CELLS DEVELOPING OVER THE FINAL APCH COURSE AND MY SURPRISE TO HAVE NOT HEARD ANY DEVS YET. TURN TO FINAL AND TRYING TO GO TO FLAPS 10 DEGS. IDLE PWR; ON THE DSCNT PATH GETTING 10-20 KT GUSTS. I STATE THAT I CAN'T GET SLOW. CAPT SAYS JUST USE THE GEAR...A LITTLE EARLY BUT SURE. GEAR DOWN. I GET SLOW ENOUGH FOR FLAPS 10 DEGS; WE ARE STILL ON THE NORMAL DSCNT AND COURSE FOR THE ILS. AT THIS TIME WE HIT LARGE WINDSHEAR +20 KTS ON THE NOSE. ABOUT 1/2 THE WIND WOULD FADE AND ANOTHER 20 KTS WOULD HIT AGAIN. COULDN'T GET SLOW ENOUGH FOR FLAPS 15 DEGS. AT THIS TIME; HIT HVY RAIN SHOWERS; TURB; AND MORE WINDSHEAR. I HAVE NO ACFT WINDSHEAR ADVISORY ON THE RADAR; BUT THE TWR CALLS WINDSHEAR ADVISORY OF +20 KTS. CAPT AND I AGREE WE ARE IN THAT EVENT. STILL AT IDLE; TRYING TO GET FLAPS 15 DEGS; I STATE TO THE CAPT THAT THIS IS WAY OUT OF MY COMFORT LEVEL AND EITHER HE CAN TAKE IT OR I AM GOING AROUND. CAPT TAKES THE ACFT. CALLS FOR FLAPS 15 DEGS...TOO FAST...WAIT FOR SPD GET 15 KTS. GUST OVERSPEED 15 KTS. FLAPS 25 DEGS; TOO FAST...WAIT FOR SPD LIMIT AND AGAIN GUST OVERSPEED. FLAPS 30 DEGS AGAIN TOO FAST...WAIT FOR SPD FLAPS 30 DEGS AND GUST OVERSPEED. ABOUT 300 FT OR SO WE BREAK OUT AND IT IS CLR ON THE AIRFIELD. JUST LIGHT WINDS; NO RAIN; AND WE LAND UNEVENTFULLY. ON ROLLOUT AND CLRING THE RWY WHILE ACCOMPLISHING THE AFTER LNDG CHKLIST; I SEE THE LAST 3 ITEMS ON THE CHKLIST ARE STILL OPEN. TAXIING TO THE GATE WE HAD SOME DISCUSSIONS ABOUT WRITING UP THE FLAPS -- FLAPS WERE WRITTEN UP AT THE GATE. I CALLED MAINT TO NOTIFY THEM OF THE POSSIBLE OVERSPEED CONDITIONS ON THE FLAPS.