Open Notepad, Word or any text editor, paste the contents of My Flow and save it.
Man, you just gave me a good idea to Backup! Anyway Flow is now a good tool to search info. So I tired to do as you said - Ctrr-A to copy all selected content of My Flow - and paste it into MS OneNote - it got it like a charm! With all that pictures and links. Now I have much more usability to search for my Flow records!
BUT! But you must manually move and move slider upto to most top in My Flow until you got needed deep of timestamps of posts. Because by default My Flow shows posts preloaded for not more than couple of last months !