How do I create a “Subscribe to my blog”button to embed elsewhere

The easiest option would be to use Jetpack plugin, which offers subscriptions.
https://jetpack.com/support/subscriptions/

However, since you’re using Mailchimp you can simply set up RSS to Email campaign to automatically trigger and send out email with your new blog post. This way you can send out your blog posts to your newsletter subscribers too:
https://mailchimp.com/help/share-your-blog-posts-with-mailchimp/

When setting it up, you would use this feed URL:
https://johngies.com/feed/