I have the embed code, but I don't know how to embed it on the server. I can embed it on my website, but I don't want it to keep linking back to Flipbook.

I don't know this for sure, but maybe you can do it the way it is explained here:
https://flippingbook.com/presentation-examples
Scroll down the page and find a heading saying 'Branded direct link'.

I see them showing it being done, just not how to do it. I am under the impression that it should be able to be on the server, similar to how my Contact forms are, but I don't even see them on the server under my projects. I believe that they are also just HTML files.

Have you tried doing this all within site designer?? no links to 3rd party no embedded code, just some custom CSS?

Mind you it sort of depends on the content, do you have an example of the book you want flipping?

I saved this as an HTML file, but what I got from them was just a string of code. I have that dropped into my website through SD, but it still links back to Flipbook and I'll have to keep a subscription to them or it will no longer work. Unless, as they told me, I could have it reside on the Coffeecup server. Attached is the Text version as I cannot attach the HTML. This is one of four that I am doing.

Your link displays a 'page not found' message. I think the link should start with https://your-username.coffeecup.com, where 'your-username' should be replaced by your actual username at CC.