No, Cloudflare will not overwrite or interfere with the affiliate links or programs you have on your site. The only time Cloudflare would overwrite a link is when you choose optional Cloudflare apps that do this.
Still not finding what you need?
The Cloudflare team is here to help. 95% of questions can be answered using the search tool, but if you can’t find what you need, submit a support request.