New 11-21: See this EmailToFlow service in action to solve an Approval Processes problem.
From Munawir ‘Mun’ Rahman in Indonesia comes a great package that installs an Inbound Email Service that takes incoming emails (each Inbound Email Service generates an email address that you can hand out), extracts the email into fields, and calls your flow. All you have to do is create a flow to handle the incoming emails with the appropriate input variables. He talks about it here, and you can install an UnofficialSF package of it below:
Version 1.0 Unlocked 2/11/21