I agree with Bob, deploying the flaps or not makes little or no difference on the gear shimmy issue. Normally, I don't even apply the brakes on landing until I am under 15kts.
I had some minor shimmy in the main gear around 28kts. I cured it by going to Good Year flight custom III retread tires from Dresser. The change in the weight was just enough to move the resonant frequency out of the speed range. I also run 45-50psi.
I still have a slight shimmy on the nose wheel, which is caused by the flat spot that occurs after a week of no flying. After rolling out and back to the runway and taking off, the shimmy motion disappears. The resonant speed is around 14kts, but will vary with tire pressure. It's not a side to side motion, it's more like an up and down motion with the front wheel. It's easy to stay away from 14kts when taxing, and it never can be felt on takeoff or landing.
Several builders have attached the reinforcement wood stiffeners to the main gear legs with success.
RV-10 - 780 Hrs
First Flight Oct 2012
Aviation Partners, LLC