How much time does it take from gout disease to recover?

Days. Gout flares resolve in several days. The overall disease tends to bring flares more frequently unless uric acid levels are lowered.
It depends. Controlling the acute attack can be fast with colchicine, nsaids and/or corticosteroids. Controlling the underlying hyperuricemia can take a long time. Using benemid, allopurinol, uloric, Krystexxa (pegloticase) to control the total body urate pool can take a long time.