From version 2.3.3 Arigato PRO, the newsletter and drip marketing plugin, now has built-in integration with JetPack contact form.
It works very similar to the Contact form 7 integration. The only difference is that you need to add the BroadFast PRO shortcodes inside the post which contains the JetPack form shortcodes. If you are including also custom fields, make sure to switch the WordPress editor to Text mode.
I have included a sample screenshot showing how one custom field and the subscribe checkbox are placed in the contact form.