A CL65 FLT CREW EXPERIENCE A FLAP FAULT DUE TO THE FLAPS BEING STUCK AT 3 DEGS DOWN.

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PERFORMING LINE CHK ON CREW FROM DSM TO CVG. DEPARTED DSM AND A FLAPS FAIL CAUTION MESSAGE OCCURRED UPON FLAPS RETRACTION; FAILED AT 3 DEGS. DSM WAS ABOUT TO BE CLOSED FOR SNOW REMOVAL. CREW PERFORMED CLB CHK AND QRH FOR FLAPS FAIL. QRH DID NOT REQUIRE A DIVERSION TO NEAREST SUITABLE ARPT WITH FLAP FAILURE OF LESS THAN 5 DEGS. TURNED ON COURSE TO CVG DUE TO DSM CLOSING. STOPPED CLB AT 10000 FT TO REASSESS THE SIT. TRIED COMPANY RADIO TO RPT PROB BUT NO ANSWER. TRIED CLBING ACFT HIGHER TO 15000 FT TO REACH COMPANY. AGAIN; NO ANSWER. KNEW WHERE WX WAS GOOD SO KEPT GOING BECAUSE DSM WAS NOT GOING TO BE AN OPTION DUE TO SNOW REMOVAL AND SNOW. RPTED MALFUNCTION TO ATC. TRIED TALKING TO DISPATCH AND MAINT THROUGH CID STATION RADIO. THIS WAS VERY CUMBERSOME AND NOT CLR. PAX WERE INFORMED OF SLOWER CRUISING SPD AND LOWER ALT. FINALLY GOT THROUGH TO DISPATCH AROUND CAP VOR. DISPATCH WANTED US TO DIVERT TO MCI BUT WE WERE ALREADY PAST THAT ARPT. TRIED WORKING WITH DISPATCH FOR FUEL NUMBERS TO IND OR CVG. THEY SAID THEY HAVE NO DATA FOR OUR SIT. THEY FINALLY ASKED OUR FUEL FLOW AND LOCATION. BOTH SIDES CAME UP WITH NUMBERS AND CVG WAS REACHABLE. GOT IN-RANGE TO CVG AND CALLED FOR CFR TO STAND BY. LANDED SAFELY AT CVG WITH ABOUT 2900 LBS OF FUEL.