Meaning: especially flat or thin. Origin and uses.
Rewrite 1: flat as a lid
Rewrite 2: flat as a snowflake
Rewrite 3: flat as a stamp
Rewrite 4: thin as the space between two dimes

Comment: There are a lot of flat, thin things, making this metaphor rife with opportunities for comparison. Have some fun with it.

More reading about clichés
What I found when I googled “clichés”:
• “All Eyes Are On…” Broadcast Writing Cliches – Using a tired cliché can give viewers eye strain.