Hi @Duncan_Anderson,
After a quick review of MyBB, you will not be able to use it with Webflow as it requires and FTP which we do not support. Now you may be able to install it through Domain.com but you will need to host it through there and there will be no direct link to it within Webflow itself.
This is geared to WordPress or other php or MySQL systems.
I would recommend Discourse for a forum as that is what we are using now for our forum.
Hope this helps and guides you in your path for your project.
Best Regards,
~ Brandon