Yes, FreeBitcoins.com does have an affiliate system. You must first register an account with the Free Bitcoins altcoin exchange (XChange) in order to receive your affiliate link. (https://freebitcoins.com/xchange/signup)
After signing up, you will be able to join our affiliate system by following this link: https://freebitcoins.com/xchange/profile/affiliate
You can also find the affiliate link in your profile or in our footer.
Simply copy and paste that link from your affiliate profile to your friends. Every friend that registered through your link will earn you 50% of their trade fees and 100% of all faucet hits for the life of their account with us!!! (Fifty percent on XChange is 0.1% & Swap is 0.5% for affiliates at the moment.) If one of your users faucets 10 satoshi, you will instantly received 10 satoshi as well.
Trade fees for affiliates are paid every 15 minutes. Faucet pays are near instant. Affiliates can view their affiliate income deposits on their deposits page: https://freebitcoins.com/xchange/profile/deposit
Here is a 30 second YouTube video showing our affiliate system being used: https://www.youtube.com/watch?v=l-TsPE5xKGI