The purpose of a flagged email is to keep those important emails that need attention ASAP where they won't be forgotten.
First, decide what shape you want your flag. A "dot" or a "Flag". Go to Settings>Mail,Contacts, Calendars and scroll down to "Flag Shape". Tap that and choose one.
Now go to the Mail app and back up to "Mailboxes". To set up "Flagged" in this menu, tap edit in the top right. Then tap the empty circle on "Flagged"
Now tap "Done" in the upper right. Now you have "Flagged" in your menu.
Now to Flag an email, open an email and you will now see a "Flag" as an option at the bottom. Tap the Flag and a menu pops up. Tap "Flag".
You will now see the email is marked with a Flag.
Now back up to "Mailboxes" and you will see you have 1 Flagged email. Tap on "Flagged" and there will be your Flagged email. You can open your Flagged email here. For options, tap "Edit" in the upper right.
Here, you can tap Trash (green) for deletion, or tap "Mark" for "Unflagging".
Again, Flagging email is a great way to not forget those important emails that need attention.
That's it! Happy Flagging!
Sent from my ancient but trustworthy iPhone 5