I have a problem with my hair being too oily too but, on the other hand, I can't wash my hair every day because it is very sensitive. So, to combat the oiliness on the days that I don't wash my hair, I sprinkle some baby powder into my hands, rub them together to distribute it evenly and then massage it through my hair from root to end. It is surprisingly effective. Another thing you can do to combat the oiliness of your hair if you chose not to wash it every day it, don't use conditioner on your roots and about 3 or so inches from your roots. You might try these techniques to see if the problem with your hairline is related to washing your hair every day. The only thing that I am concerned about is the possibility of the baby powder drying out your hairline further and causing more flakiness. Have you tried applying some moisturizer to the visible portions of your hairline? Perhaps it is just really dry.
I wish I could be more help but, the only thing that I have that is similar, that I can be of some help with, is rhw oily hair every other day issue.
Sorry! Take care and keep in touch!