I put together a cheat sheet to help assign Scott numbers to the various Four Flags booklet stamps. The main reason was to see if Scott nos. can be assigned based solely on the straight edge configuration (side and number), and avoid trying to determine if an on-paper stamp is the thin paper ATM variety (Scott 4706-4709). Unfortunately, that goal was not entirely successful. However, here is what I did discover.
At a minimum, you need the following to properly assign a Scott no. to MOST Four Flags booklet stamps:
1. Design (Freedom, Liberty, Equality, Justice)
2. Number and sides of stamp with straight edges
3. Flag width as measured from LL to LR corners of flag
4. In no cases do you need to determine color of the dots in the stars (which can be a pain), except as a confirmation
The exception is that some of the Ashton-Potter (P) printed stamps require determination of paper thickness to properly assign the Scott number. On mint and off-paper stamps, this is easy because the stamps are so thin and translucent. On-paper stamps will require comparison to other on-paper stamps confirmed to be printed on paper with normal thickness. It helps if the stamp is affixed over some printing on the envelope (e.g., "Place Stamp Here") to evaluate translucency.
I don't own a device to measure paper thickness, so I won't comment on that method.
I made an assumption that the ATM pane is only available in the configuration displayed a few entries above this one.
Below is the cheat sheet I created. I have a pdf version available upon request. Send PM if interested.
P.S. L=left, R=right, T=top, B=bottom