A CRJ900 Flight Crew landed with flaps up following receipt of a FLAPS FAIL warning.

Narrative

Got a flaps fail caution during landing approach. FO(First Officer) called ATC and told them we needed to cancel our approach. They told us to turn and climb to 4000. We did and ran an after take off check and advised ATC of our problem. Fuel after the go around and level off was 2300-2400Lbs. I flew at 210 while the FO worked through the checklist. I took the radios for awhile; while the FO was in the flap fail checklist. I requested ARFF stand by but did not request priority. There were several reasons we were not ready for an approach. We had to rebrief the failure and new runway. Although fuel was tight; it was not critical and if we requested priority it may have pushed things along too fast. We advised Dispatch of our problem. We also advised the Flight Attendant. We asked for a 25 mile final as I believed the timing would be sufficient to finish up the checklist and brief. At 20 miles out on a right downwind we advised ATC we were ready to turn in for base turn as the brief and checklists were within a minute or two of completion. We received a right turn; then another; which I thought was a right for final but may not have been; and were given a new heading; more towards a base turn. We landed uneventfully; advised no further assistance was necessary; and taxied in. Landed with 1850 in the tanks. Comments: The aircraft had 3+ write ups for flaps in its history.