What is the minimum windspeed needed to make a flag wave?

According to "Science Bob":

"5 mph is just a breeze. 15 mph will make a flag wave, 25 mph winds can turn umbrellas inside out."

sciencebob.com/lab/weather.html [no longer exists]

According to the Beaufort Scale it is between 12-19 kilometres per hour that a light flag will unfurl.

http://www.hwn.org/resources/bws.html

American Flag:

Nylon flag or cotton flag? Embroidered or printed? One piece or sewn together stripes? All of these factors will greatly changed the amount of necessary air volume to cause Old Glory to stand proud.

USING FLAGS TO ESTIMATE THE WIND SPEED

You can use a ordinary flag to give you a good indication of the wind speed. Take a look a the table below.

Bft = Beaufort Scale Wind Speed
0 Bft - I assume you can guess what this looks like.
1 Bft (1-4 mph) - the flag only occasionally flips open, the outer end hangs lower.
2 Bft (5-7 mph) - the flag is mostly extended, the waves are deep, a large portion of the outer top corner flips back and forth.
3 Bft (8-11 mph) - the flag is completely extended, the waves are faster and smaller than 2 Bft.
4 Bft and Up (12-18 mph) - the flag is still completely extended, the waves are faster than 3 Bft. The changes from 4 Bft. and up are more subtle and harder to distinguish from each other, but this is of little concern since the choice is not what kite to fly, but whether to fly a kite at all.

http://hwn.org/resources/bws.html
https://education.nationalgeographic.org/resource/beaufort-scale/