Does this support normal Git links? If so, you could simply link to a Gumroad or similar site and have that send a Heroku Button link with a customized git repo where they can deploy from.
I imagine you need to set up your app to use Heroku. It's not very hard but beware that you can't write to the filesystem with Heroku so that would need to be factored in to the functionality of quite a few apps.
You can write to the file system, it's just not persistent across dyno restarts or shared across running dynos. Writing out for in-request work is fine.
Right now buttons only work with source code hosted on GitHub (although the button can be added anywhere). We want to extend that to other source code hosting services, though.