First, a warning. Try not to give them real long grass clippings. When they eat grass while foraging, they bite off fairly small chunks. If they eat long grass clippings, it can give them an impacted crop by getting twisted in their crop where it cannot pass on to the gizzard where it is ground up. The recommendation us to have the clippings under 2" in length. It doesn't happen that often, but chickens do die from an impacted crop. if you use a mulching mower, they usually get chopped up enough. Or run them through two or three times. Or mow often enough that it is not an issue.
Now that the public service message is out of the way, how long to compost them before you use them depends on a few things. Part of it is how often you turn them, part is how moist you keep them. You don't want them soaking wet but they need to be slightly damp. If they dry out, it can take years for them to break down. Part is how hot it is. They break down faster in the heat than if they are frozen. It makes a difference if they are piled on the ground or if you have one of those barrel composters you can turn. If they are turned and have the right mix of carbon and notrogen, they will heat up and cook the seeds. But if they are piled in the the ground and turned, it is really hard to get all seeds cooked.
In short, there is not easy answer to your question. If they are kept damp, you have regular weather, you have a reasonable mix of the carbon and nitrogen materials (called browns and greens although they have nothing to do with color), and turn them a couple of times, you can probably use them in three months or so. If you have them in a barrel composter and keep everything in ideal conditions, you might be able to use them in as few as three weeks. If you are like me and don't work at it too hard, it could take 6 months or more.
Good luck!