Is it permissible for an affiliate marketer to purchase the product they are marketing through their own link in order to earn commission?

There is no objection to you marketing for stores and hosting companies as long as you do not stipulate that the client must not be a marketer. However, if they prohibit marketers, then you must abide by their condition, for the Prophet, peace and blessings be upon him, said: "Muslims are bound by their conditions."