My mother always says that one should not wash the dosa kal too much; otherwise, this kind of problem will happen.
Are you sure it is problem with yr kal or could it be becoz of batter(excess of urad dal)?
Grease the kal with oil or spray and evenly spread with tissue; make a small first dosa and then, start making the usual size of dosa. I also noticed that if I pour the batter on the black grease(edge of the kal), it would stick and would not come. Also, try dipping the spatula in water before flip over the dosa to the other side.