When I have really strong crosswinds, I generally leave the flaps up becasue I am goign to keep some speed up to maintain better control, and once I am on teh ground, I want as little lift as I can get - to keep the airplane from trying to lift back off. The flaps will lower stall speed, and I actually want a HIGHER stall speed to facilitate killing the wing?s lift.
I also use a wheel landing with significant crosswinds becasue I want more speed for better directional control until I have planted the airplane. Then with no flaps, it is less likely to balloon back off the ground if I take a sudden gust, because of the higher stall speed. Less lift, less likelihood of lifting back off.
BTW - I don?t really consider it ?windy? until the wind is sustained over 20 - for 15 knots within 45 degrees of the runway, I would probably still be using flaps.
Usual disclaimers apply - this works for me, YMMV, and I don?t give flight instruction over th internet!
Paul