This actually has more to do with Rails and/or Sinatra than it does with Heroku. You have to enable IFrame support in your headers explicitly.

With Rails you can add this to your config/application.rb file

config.action_dispatch.default_headers = {
    'X-Frame-Options' => 'ALLOWALL'
}

In Sinatra you add this declaration in the configure block

configure do
    set :protection, except: [:frame_options]
end