Basically I want to create a one page magento checkout site (similar to this site: https://store.whistle.com/orders/new) where the product and checkout are one the same page.
Is that even possible? If you don't recommend it, why?
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How can I put the onepage checkout on a CMS page?
You can't. Well. Maybe you could... maybe iFrame it? But I'm not sure that's what you actually want.
What you're probably looking for is one of the many one-step checkouts that are available for Magento. Here are a few:
Those are both paid extensions. Here's a free one: