You don’t need a website to collect emails. If you blog on Medium, you can use Upscribe’s embedded subscription form that were created especially for Medium. They are the only embed option for Medium and their forms convert well, but they started to charged rather steep monthly fees lately, so this is not a free option any longer. They charge $9 per month for the lowest plan.
If you use their lowest plain, they will collect emails for you, but you will have to export the new emails manually to MailChimp. If you want to sync the form with MailChimp to get the new emails on your MailcChimp list automatically, Upscribe charges $25 per month for that. I see this as outrageously expensive.
Since they are the only ones who have created embedded forms for Medium, however, I guess they can get away with it — but this is a great business idea, just create an embedded form option for Medium and sell it for half the Upscribe’s price.
You do need an email for MailChimp, though, since MailChimp sends out your newsletter using your email address.
Best of luck with your book!