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Here's a photograph of Patton's jeep, originally from Wikipedia and dated 1st January 1945. I would say that the flags are too small to be noticed by a pilot. Driving in a jeep, used for many other purposes, would be much less conspicuous than being in a staff car, so I think that Patton would have been relatively safe, certainly from air attack. Patton also used a Dodge Command Car, which would have been more conspicuous. I don't know which he used more often.
The flags in the movie still appear to be around twice the linear dimensions of those in the photo above, so in partial answer to the question:
Yes, generals' vehicles were flagged, but not as prominently as the movie 'Patton' would have you believe.
Upvote:0
I'll answer the "Did this ever happen?" part.
On 6th April 1941, British General Richard O'Connor and Lieutenant-General Sir Philip Neame were captured in their staff car by a German patrol on their way from Maraua to Timimi, where their headquarters had been moved. However they would probably have been captured no matter what pennants they were flying.
Upvote:32
This is called a pennant (I hope I translated that correctly, "Stander" in German).
Flying a pennant has disadvantages (as you mentioned), but it also has advantages. Allowing messengers to locate the commanding officer quickly is one of them. A boost to morale, knowing that your General is right there. I don't know WWII US army procedures, but in the German Bundeswehr a car flying a General's pennant will usually not be stopped at checkpoints either, allowing for speedy travel.
Of course it becomes a problem the higher enemy activity in the area is, to the point where the disadvantages outweigh the advantages. That is for the General to decide. I don't remember the movie scenes in question, but I can readily believe that Patton didn't give a damn.
As for "did something bad happen to Generals", I'd cite Erwin Rommel who was seriously injured in a strafing attack. Whether the pilot actively identified his car as "uh, this looks important" or just shot at "random car on the road" is unknown though.
You might want to note that naval traditions are even more pronounced in this regard. Since ship-to-ship communication was done by means of flags, it was imperative that every ship in the fleet knew which ship carried the admiral, at all times and at a glance. So even in the midst of battle, the flagship would be easily distinguishable because it would be flying the admiral's flag -- even if that might mean drawing additional attention to itself.
Wikipedia: Replica of Patton's command vehicle with exactly those pennants