I wanted to know how long do I have to take anti-androgens? forever? Or until I'm done with my electrolysis treatments?

Antiandrogens are usually given until the source of excess production is removed or slows its production. This usually doesn't happen without surgical intervention or until many years have passed. Therefore, these drugs are usually prescribed for the long haul.

Taking antiandrogens while undergoing permanent hair removal will probably increase the effectiveness. You should speak with your doctor about the option of comcomitant treatment to assist with hair rmeoval, since antiandrogens have powerful effects on the entire body, some of which you may not want.