B737-700 flight crew reported retracting gear before flaps during a go-around procedure.

Narrative

Landing gear lever moved up before flaps on go-around.My FO was flying the ILS PRM (Precision Runway Monitor) [for Runway] XXL into ZZZ. We had completed all briefings including the PRM brief and had monitor frequency setup in the #2 com. During the approach the winds were a direct 20 knot tailwind to about 2800 ft; so that was inside the G/S intercept alt. IMC conditions started about 4000 ft. with airport reporting east winds and about 300 ft. broken layer. Good visibility. I vaguely remember my FO reaching up to the MCP panel; on G/S fully configured with flaps 40; we were about 1200 ft. to 1400 ft. descending. I'm not sure if he pushed something or not but suddenly we lost FDs on both sides. We both hesitated with comments like 'what just happened?'. At the same time the wind was shifting to a 20 knot right crosswind. We then heard monitor Controller say something about our LOC track and I glanced down and saw we were drifting just slightly to the left off of the LOC. I said let's go around and then transmitted on Tower 'We are going around'. I couldn't get our call sign in there because I was distracted with the unfolding situation. My FO started slowly putting in power and I don't think he pushed TO/GA. Two seconds later he called landing-gear up and tower ATC gave us missed approach instructions; all at the same time. I looked to see positive rate and I selected gear up and right that second I realized flaps were still extended and I did the procedure out of order. We had good airspeed and did not exceed flap speeds. We then selected flaps 15 and then worked at cleaning up flaps and flying the missed approach instructions. We got vectors back around for another uneventful approach to landing.Debrief notes: I should have helped my FO with proper missed approach call outs but was so distracted at the moment getting my thoughts straight. Because of letting myself be distracted I missed the flaps to 15 first. 'Aviate; navigate; communicate'. I know better than to skip this. To help myself and my crew member; I will remember to make sure we brief the note section on the JEPP approach plate if the PF doesn't cover all the notes. In the notes on this approach it says FD or AP required during PRM. These are good 'flag post' items to help remind me to discuss missed approach procedures if we lose those and then execute a go-around without hesitation; and then do it methodically and correctly. The winds made this a difficult approach. Remember to be ready for anything.