I wrap my hair the traditional way when it's straight as well. I don't get any breakage. I always put a small amount of oil on my ends, wrap with my paddle brush and then put on a mesh wrap before adding my silk scarf.
Two tips I've learned along the way:
Hair should be bone straight. I find that the straighter the hair from the initial press, there will be less lumps/bumps in the hair for the brush to snag and break.
Hair should be well lubricated (but not overly oily) to cause less friction when you wrap as well.