Stop, drop and roll.
If you have a fire blanket handy, wraps it around the person whose clothes are burning. Otherwise a wet blanket can help.
In spite of what you may have heard, fire extinguishers can also help. Yes, even a CO2 extinguisher, as long as you don’t keep the jet on the person for too long.
Theory aside, I’d recommend using whatever you have at hand, but stop, drop and roll is a good rule.
Stop: Stop running around shrieking and waving your arms.
Drop: Drop to the ground.
Roll: Roll around. This will help smother the flames, as they will be deprived of oxygen while underneath you.
Once you’re on the ground, people around you can help with sand, water, wet blankets, wet towels… Whatever is available.
Actually putting out burning clothes isn’t all that difficult. The problem is that synthetic fibres tend to melt, and the melted globs of plastic-like “Lava” cause and worsen existing injuries simply because they are fricking hot and make it impossible to get clothing off the injured person in one peace.