Of course the scarves/streamers/ribbons attached to the helmet do nothing to prevent chafing. 
Given that, as I guessed in the OP, scarves were used to wipe the goggles, it seems that the only function of a scarf attached to a helmet would be that. (And it looks flash.)
(Icerigger: What was the surprise in the video?)
Well, the Spitfire. When I first watched this video a few months ago I did not pay attention to the title so I was a very Holy Shit! moment when the Spitfire appeared. The Camel sure does rock a bit on the ground when firing up.
Aha! I knew the Spit would be there. 
Yeah, that rotary engine has a lot of torque.
If you read the Biggles books set in WW1, there were always references to wiping the goggle of castor oil, although scarves weren’t mentioned (as far as I can remember).
The author (W.E. Johns) was an aviator. He ended up being shot down and thrown into a prisoner of war camp.
Generally - yes. Pilots would “personalise” their planes to deliver improved performance.
“Flying Fury” by James McCudden VC talks of this.
This question came up again just now.
Anyone have a definitive answer?
Note that I’m talking about the scarf or ribbon attached to the top of the helmet that appears to have no function, not the one worn around the neck whose function I assumed everyone knew (first sentence of the OP), and which has been explained in this thread.
Read some where that it identified the flight leader for each element.
Who to form up on, etc.
Maybe a few other things during training although the aircraft had a streamer for a first solo flight and / or a student pilot.
Remember, no radios for them in those planes.
Some of this carried over into WWII training also, especially on the Stearmen trainers.
This high technology is current still, a variant of which is still seen on sailplanes (gliders) today. It consists of a piece of string taped to the outside of the front of the cockpit.
Good photo at How Gliders Work.
I think that streamer on the top of the pilot’s head would be easier to see in certain conditions. Think of the sun angle and varying weather conditions, although they tended not to fly in really bad weather.
Although they used a lot of hand signals, it could have been used as a signal to attack, or to regroup after a dog fight.
I wrote a couple of papers on WWI, but I’ve never seen anything about that, interesting question.
And RFC planes were generally painted alike, with no great personalization like the Flying Circus guys.
I liked the deHaviland Viper parked next to the Camel. Back in the early days of eBay I almost bid on John Travolta’s Viper, when the bidding was still around $7500, but didn’t because, in the extremely unlikely event that my bid of $7501 won, my inability to pay for it would result in negative feedback! :rolleyes:
It was as recently as when I got out of the Air Force in 1992. Each squadron had their own scarf, which had to be folded a certain way and worn with our flight suits.
I just did a little googling and didn’t find anything conclusive.
Streamers were commonly used do denote flight leaders, but those were normally attached to struts.
The only advantage I can see for having one on the helmet is that it would be easy to unfurl or retract as needed.
Just my speculation, but if the flight lead was shot down, an alternate could easily unfurl his helmet streamer after a dogfight.
Towards the end of the war, some of those engagements were getting very large, with formations of over 80 planes per side.
So the need to improvise inflight communications was certainly there.
I wonder if the streamer isn’t a Hollyweird invention? I can’t remember ever seeing any era photos of WWI pilots with streamers. Only in the movies.
I also question why any real-life, combat pilot would attach such a drag inducing device to their helmet. At open-cockpit, combat speeds, of 60 to 100 mph, the buffeting would have been tremendous and their neck muscles would tired very quickly. It would be like trying to hand hold a streamer or handkerchief out of a car window at highway speeds.
The Hollywood idea is just as plausible as what I was tossing around.
Unless it was a thin ribbon, it probably would be a hindrance, and annoying at the very least.
And the military would never have anyone do something like that…
Streamer tied to a strut makes a guy a special target = bad. (can’t remove it from bad guys vision out there)
Streamer tied to top of helmet is a known place to look, can be pulled in during actual fighting to remove target from leaders plane, can be added to second in command’s top knot if number one had to use his parachute. So to speak… :eek:
Ex Pipeline patrol pilot here, Held many small sand bag, streamered notes to throw to folks on the ground, not as hard to do as flying you arm out a car window IMO.
Hit more than one guy in the chest. Bawahahaha I had to lift my left wing up to keep from taking his head off but I nailed him center of mass. We used to have some fun. 
Very belated response to this statement, but according to the book I had to study for my promotion test (didn’t make it this year, maybe next year), one common complaint that US Army leadership had of pilots during the first world war was their blatant disregard for uniform regulations.
Because they didn’t wear their spurs while flying their planes. 
The military has always been a slightly absurd culture.