Cloudflare can be used with Customer Specific Pricing, you just need to add a page rule for it within Cloudflare.
- Log into your account at cloudflare.com.
- Select Page Rules.
- Select Create Page Rule.
Under "If the URL matches:", enter:
Note: Replace (your-domain) with the URL you use to get to your store: (ie. mystore.shopify.com).
- Select Save and Deploy.