You do put the flag up on the mailbox if you're sending outgoing mail.
The red flag on a curbside mailbox is for sending outgoing mail.
When you have outgoing mail to send you put the mail in the curbside mailbox and then raise the flag.
The red flag on the curbside mailbox signals to the mail carrier that you have outgoing mail in the mailbox.
Then the mail carrier will stop at your box and remove the outgoing mail to send it off and then they will lower the red flag.
So even if you have no mail coming to you directly on that day you can send outgoing mail from your mailbox and the mail carrier will pick the mail up.
Just make sure to raise the red flag so they know the mail is in the mailbox for outgoing mail.
I've mailed letters through my mailbox before and the mail carrier always lowers the flag down after they get the mail out.