EMB-145 Captain reported poor decision to delay go-around procedure to workout a flap fail message led to a hurried process. Captain reported an earlier go-around would have provided more time and fuel to complete all procedures.

Narrative

During a visual approach to Runway XXL in ZZZ the CP (PF) called for gear down and flaps 9 at 240KIAS. The gear extended normally but a flap fail message displayed on the EICAS (engine indicating and crew alerting system). The FO (PM) began running the appropriate QRH (quick reference handbook) procedure; but due to the limited time available; the crew elected to conduct a go-around. During the go-around; the crew observed that the flaps remained deployed at 3 degrees. While on downwind; the FO (first officer) completed the QRH procedure; reloaded the avionics for an approach to Runway XXR; and completed a briefing to the Flight Attendant. The Captain conducted a partial flap landing; exiting on the taxiway. No further abnormalities occurred during the taxi in. The issue was reported to maintenance and written up at the gate upon arrival. Suggestions: In the future; I would initiate a go-around sooner. The FO was very familiar with the QRH procedure due to recent previous experience with this malfunction and was able to complete most of the checklist while continuing the approach. However; there was no reason to hurry the process when a go-around provided ample time to finish all checklists and the flight still arrived at the gate on schedule and with greater than the planned reserve fuel on board.