Hi @Anonymous,
Can you share a screenshot of your Flow configuration?
It sounds like this is not difficult, you can add two columns, one to record whether the message contains an attachment, and the name of a record attachment.
Use variables to save the names of all attachments in a String and then insert them into the table.
Image reference:

Expression:
if(triggerBody()?['HasAttachment'],'Yes','No')

Please take a try.
Best Regards,
Barry