Yes, they are standardized to some degree.
I have wondered about this myself. In the Uncle Sam's Misguided Children gun club, Uncle has control over everything, and the flags may well be identical from one base to another and over decades of time.
However, similar flag angle charts are shown in data books used for competition by all comers, and so I think there must be some standard material and weight.
But what if it is raining and the flags are wet?
This is where your face, and tree branches, and a few blades of grass, and a Kestrel wind meter come in handy. I see many folks on the line with a piece of yarn tied to their spotting scope stand.
Also, on a military shooting range there are usually flags at every yard line on both sides of the range. Sometimes, say you're at the 300 yard line, you will look around and see that the flags at the 200 yard line are streaming at 4:00 to the right, but the flags at the butts are streaming at 5:00 to the left. Or worse yet, the flags on the right side of the range are streaming left, and the flags on the left side of the range are streaming right. EEK, swirling wind on the range... Some folks have been known, under these conditions, to wait on their first shot, and watch the targets come up for all the other shooters' first shot... If they can see a trend, say many other shooters' first shots came up out to the right, then they crank in another click or two left and then shoot.
Judging the wind for the first shot is one of the toughest things about long range shooting. It just takes time on the range, getting experience in varying conditions to get good at it. After the first shot you get a good idea of how far off your estimate was, and correct from there. But the wind is seldom ever constant so you need to be able to read the shifts for each shot and adjust accordingly, and of course these adjustments are dictated by the bullet weight, ballistic coefficient and muzzle velocity you are shooting. A light shifting wind that you could just ignore when shooting 175 grain .308s will have you sawing back &forth on the windage knob if you are shooting 55 grain .223s.
Once you have made your best estimate of wind, you need to convert that into clicks of sight adjustment for the rifle and ammo you are using. Remember that any correction chart shown in a military data book is specific to that rifle and ammo. For example, you may be looking at a data book for the M16A2 shooting M855 62 grain ball ammo. If you are shooting an AR15 with 80 grain Sierra Match King bullets, your windage corrections will be different.
The flag angles are only one way to get an estimate of the wind velocity.
Make no mistake, by taking an interest in accurate shooting you have been infected by a disease and there is no cure.
Oh, and by the way, none of this advice is free, for whatever it's worth. If you have ever paid a dollar in taxes, you already paid for me to spend a lot of time on the range shooting free ammo through rifles that I didn't own. Even though I'm retired I still have a duty to pass on whatever I may have learned...