Flair are the rewards you get from completing quests, which will show up on the left of each of your posts.
Currently there's a 14 flair limit per category. So 14 main quests, 14 side quests, etc.
If you manage to get more than 14 types of flair in a category, you can still see all the ones you've earned on your user profile page by clicking on your name.
But, if you have more than 14 not all of them will be visible. If you want to make sure your favorites are display you can manage your flair via the User Control Panel. This can be found via the menu at the top of the page.
Click over to the 'Profile' tab and select 'Manage profile flair' from the list on the left.
Now you can click the star button next to your favorite icons to make sure they're listed first. Though they will still group themselves by type. It will also automatically fill in icons up to 14 from those you have left.