I have experience with direct to consumer growth, referral growth and WOM for startups and large corps.
Your plan makes sense but I think you could test a few key elements to identify the most effective approach for your goal.
Is your primary goal to get more people to view the site through referrals or is the goal to drive more people to complete the purchase of products?
- Do you have the ability to give a product as the goal? EG. A one size accessory for referring 3 friends? A tangible product may work better than a discount in this case.
- I have found that giving users a big discount/offer to give to friends is most effective especially when you want them to share Fashion.
- You can create a feedback loop to confirm if the offer is correct or if there is something else preventing referrals.
- Do you have cart technology on your site? If you do there are a number of plugins that can help you test and manage this type of hack to avoid the potential hurdle of facebook sign up.

I think I probably need a few more details to be really useful on this question. I'm happy to chat if you'd like to arrange a call.