In general, Go Around (or TOGA -- TakeOff/Go Around) mode is armed or selected during takeoff and approach. As CA indicated, details vary among airplanes (e.g., Go Around may be automatically armed when Approach Logic is satisfied or when Approach mode is selected).
Flap or gear selection should not inhibit Go Around. If another mode (e.g., VNAV and/or LNAV) is armed when Go Around is selected, Go Around will transition to that mode when the appropriate conditions (e.g., altitude) are attained. Go Around can be done in either Autopilot or Flight Director mode, or with both turned off (since Go Around is also an AutoThrottle mode).