(n.) an unhealthy obsession with flags
Vexillomania is an abnormal love or desire for collecting or displaying flags.
It’s also one of quite a number of English words that exhibit the same root. Vexillum was a Latin word for a flag, banner, or a military ensign, and it’s from there that this word derives alongside vexillology (the study of flags), vexillarius (a Roman standard-bearer), vexillation (a division of troops or cavalry under a single flag), vexillographer (a flag designer) and vexillator (a performer in a mystery play carrying a flag or banner).
Go back far enough, and words like these can be traced back to velum, a Latin word for a fabric covering or some similarly large swathe of fabric, like a sail or curtain. It’s from there, with a little help from French, that English has picked up the word veil.