Can you put flyers in mailboxes if the mailbox flag is down?

No, the flag position changes nothing. The mailbox flag only signals to the carrier that there is outgoing mail to pick up. It has no bearing on what may be placed inside. A residential mailbox is reserved for postage-paid USPS mail whether the flag is up, down, or missing, so dropping in an unstamped flyer is illegal either way.

• Flag up, down, or absent: none of these permit unstamped material inside.
• The flag's only job is to tell the carrier there is mail to collect.
• The mailbox stays protected as USPS territory at all times.
• Use compliant methods instead: door hangers, bulletin boards, or postage-paid mail.