Maybe an inch or so? If we haven't mowed in a long time (i.e. first mow of the season) we usually toss all that in the compost bin, because we can get some pretty long pieces, like 6", and I've seen my chickens try to choke those down regardless of the length.
Maybe it makes a difference what type of mower you use. My mowers cut and recut the grass clippings on their way to the bagger. I don't know if it's even possible to have a grass clipping 6 inches long on my mowers. But, I typically cut my grass when it is about 4 inches tall and I have the mower set at about 2.5 inches. In theory, the longest grass clipping I would ever see should be the top 1.5 inches.
Fortunately, I have never seen any crop blockage due to eating grass clippings in my birds in the 3 years I have been feeding grass clippings to them. I wonder if there have been any studies on chickens eating grass clippings, and what is more likely to cause a blockage - long grass or just the quantity of grass they eat?