What membership plugin are you using? I would think that most membership programs have affiliate tracking. Each member is assigned an member id and that id is used in an affiliate redirect link to track each member. An affiliate program is a membership that affiliates register for.
So, read your documentation and see if they have an affiliate link configuration.
The problem with self hosted affiliate program is that affiliates don't have anything other than your word they will receive the commissions they have earned. You can use a service like JVZoo.
But affiliates and vendors are starting to see some of the problem with the JVZoo system like affiliates having to be approved for each product in a sales funnel before they will receive commissions. Or delayed commissions not being paid. Plus security is suffering by not being able to prevent fraud from affiliates.
So it may be better to slowly build your own affiliate program and as your reputation gets better known, you will be able to attract better and better affiliates. Before you know it, you will have your own affiliate army.