As far as I know - it's forbidden to use affiliate link on Facebook, although some people say that link shorteners work.
To get more traffic to your group you need to ask already existing members invite their friends, share, etc.
Do you have a website/store/facebook page? You could ask your current followers to enter the group too. Otherwise maybe it would make sense to create a Facebook page (open obviously), get followers there, and then make a post about your closed Facebook group. If it's a post - you can promote it on FB.
Check this post - quite informative.

You business model is totally wrong. FB is good for brand awareness not conversions. Some people will disagree to this statement but its all I have seen.

First of all FB will ban you if your are promoting affiliate links and then if you really want to get new members than share some interesting conversation, contact to other members in related groups. Make your group more hip and happening.

Affiliate links don't work on Facebook. You might get banned if you continue posting affiliate links. For making your group bigger, simply ask your group members to add people who might be interested in the group. Interact and engage with your group members.

Loren

What's the incentive for people to join the group? How are people bettter off for joining your group?

You need to look at what you're offering that would make people want to join.

You may request your FB friends to invite people who are interested to join your group.