With the guidance from AlanPs1 above here is the solution I found that worked OK for my needs.
Export Email > Create File > Get File Content > Send Email > Delete File (to clean up).

Step 1 was to export the email. My flow is triggered when a new mail is received and the ID that's exported is that triggering email. This value is used in step 2 as the file content.

Step 2, Create File. I picked a folder that should be out of the way. It's really just a temp location since I'm going to delete this file at the end anyways. File Name I don't think matters, so I used the message ID of the original mail. File Content here is the body of the "Export" in step 1.

Step 3, Get File Content of the newly created file in step 2. This will be the file content of the file attached to the email.

Step 4, Send the mail with the attachment. As AlanPs1 points out above, the '.eml' extension is important and the Body of 'Get File Content' will be the content of the attachment.

And the Step 5 is the cleanup to delete from the site the Id of the file from Create File in step 2.
Hope this helps. Thanks.