What education does a parent need to homeschool children?

It depends on the state I think. In Indiana, for example, there are no laws concerning that. You can homeschool your children even if you did not graduate from High School.

Answer:

It is new information for me that parent's education matters for their kids enrollment. There would be some laws for some states out there but as far as distance learning is concerned then there are several institutes like UK Open College that does not place such compulsions for registrations. They offer flexible registration with better education.

You just go and check their policies for detailed information.