Similar to JorgeCarvalho's suggestion to allow SharePoint mailboxes to be targeted by the Office 365 Outlook integration (https://powerusers.microsoft.com/t5/Flow-Ideas/Flow-to-support-SPO-Site-Mailbox/idi-p/5982)
It would be supremely useful if we could select shared mailboxes too (and even resource mailboxes too) for Flows. At the moment, personal credentials are chosen (shared mailboxes don't have authenticable accounts).
You can now both trigger on shared mailboxes and send mail from shared mailboxes. Read more here: https://flow.microsoft.com/blog/canada-mailboxes-aad/
It is working. O365 shared mailbox have possibility to add password (Admin Portal user screens) and in flow you can add connection with shared mailbox. Just log-in in pop-up with user/psw from shared mailbox. Shared mailbox should have beed added to someone. But flow - someone is sending mail to this mailbox and flow read it and do something - is working.