Your best bet would be the following: Coat the raw chicken in flour then dip it in the egg wash (eggs beaten together with a bit of water), then finally cover the chicken in your dry rub. This will ensure that the dry rub will stick to the chicken in hot oil. I would also recommend seasoning your flour with salt and pepper.
Cooking times will vary by the thickness of your breast/legs. Typically it takes about 7 minutes at 350 degrees to cook through. For even cooking you might want to pound the chicken breasts out a bit with a meat mallet so the breast is an even thickness.