A wrapped flag is the single most common complaint in this trade, and the single most misdiagnosed. People replace the fabric, and the new one wraps too.
What is actually happening
A flag has to point downwind. If the whole assembly can rotate, the wind does that for you — the flag swings round and streams cleanly no matter which way the gust comes from.
If it cannot rotate, the fabric has nowhere to go but around the mast. Once it has wrapped one turn it is held there by its own tension, and it stays wrapped until somebody walks out and unwinds it by hand. Every gust after that tightens it.
The three things to check
First, the base. It should have a free-turning collar, and you should be able to spin the pole by hand with almost no resistance. A rusted, gritted or seized swivel behaves exactly like no swivel at all — rinse it, dry it, and try again before replacing anything.
Second, the sleeve. A flag sewn too tight on the pole cannot settle. It should slide down and sit without being forced.
Third, the height. A very tall flag on a short pole section run has more fabric than the rig can control, and it will bind even with a good swivel.
Fixing it
In most cases the answer is a new base with a working swivel, which costs a fraction of a new flag and takes a minute to swap. Keep the fabric; there is usually nothing wrong with it.
If the site is genuinely exposed and the wrapping continues, drop a height. A 3.4m flag that flies all year is worth more than a 5m flag somebody has to unwind twice a week.