B737-800 CREW ENCOUNTERED SEVERE WINDSHEAR ON APCH. THE ACFT HAD A FLAP OVERSPD. THE CREW MADE A GAR. DECLARED MINIMUM FUEL; AND DIVERTED TO THE NEAREST SUITABLE ARPT.

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FLT INTO GEG. RELEASE WAS NO ALTERNATE. SCHEDULED TO LAND WITH 7500 LBS OF FUEL. WX AT GEG 6000 FT OVCST; 6 MI VISIBILITY; WINDS CALM. THERE WERE NO RPTS OF TURB OR GUSTY WINDS. VREF 138 KTS; TARGET SPD 143 KTS. ONLY HINT OF POSSIBLE WINDSHEAR WAS A SIGMET WE RECEIVED WITH ZLC FOR SEVERE TURB IN MT; BUT NOT WA. LIGHT TO MODERATE TURB ON APCH. INCREASED TARGET TO 148 KTS. ON FINAL AT ABOUT 1500 FT AGL; AIRSPD DROPPED OFF IN A GUST TO ABOUT 130 KTS AND THEN IMMEDIATELY INCREASED TO ABOUT 165 KTS. AIRSPD STABILIZED FOR ABOUT 10 SECONDS AND THEN ANOTHER GUST HIT. AIRSPD DROPPED OFF INSTANTANEOUSLY TO ABOUT 128 KTS. WINDSHEAR RECOVERY WAS INITIATED BY PF (THE COPLT) AND AIRSPD INCREASED INSTANTANEOUSLY TO ABOUT 195 KTS. PREDICTIVE WINDSHEAR WARNING RECEIVED DURING GAR. DIRECTED TO PSC DUE TO INSUFFICIENT FUEL TO SHOOT ANOTHER APCH AND STILL DIVERT TO PSC. DECLARED 'MINIMUM FUEL' AND LANDED WITH 3700 LBS OF FUEL IN PASCO. WROTE UP FLAP OVERSPD. UNABLE TO CONTINUE TO SLC OR GEG DUE TO CREW DUTY DAY.