Can I ask why you put down the weed block cloth? Weeds in the run are a chicken's best friend! You may find that your birds dig down and shred that cloth. Are you talking about DL in the run, or in the coop? I'm still working on getting a functioning DL in the coop. It works best if it can be done on a soil floor. It's almost impossible to do it wrong, in that case, as long as you have good drainage. On a wood or linoleum floor, it can be done, though more difficult. Leaves, grass clippings, some wood chips (not a lot) weeds, and other yard debris, with a bit of soil to inoculate it. Then, you need to be sure that you have the right amount of moisture, without rotting out your floor or walls.
With chicks in the brooder, I use shavings for convenience. As the litter gets soiled, I just toss more shavings on top. You can do the same with leaves, grass clippings, hay... what ever you have available. Remember that many of these bedding materials have a tendency to mat down, creating a layer that is difficult to break up. So, it's good to do very small layers and vary the materials, so they end up being a mixture of shapes and sizes.
In the run, be sure to toss any old bedding being removed from the coop. Wood chips from a landscaper prove to be a valuable commodity in my yard. We bag all grass clippings. There are never enough of them. They go in the hoop coop, run, garden, orchard, lasagna bed, and on the hugelkulture mound. Same with leaves. I collected 100 bags from a yard in town last fall. Back breaking labor when those contractor bags were full of wet, frozen leaves, but well worth it, as my yard doesn't produce any where near enough. Same with wood chips. Had at least 21 cu. yds. delivered. Need to get more this summer.