Wouldn't the chickens dig up the landscape fabric? It seems that the fabric might be a problem to work around if it were exposed.
Weeds aren't likely to be a problem with the chickens eating everything in sight. When they kick the gravel out into the yard, will it be a problem for mowing?
I used river sand, larger than typical sand granules, but they worked it into the soil after several months. Everything still drains well, but it is no longer a cover for the soil in the run.
I don't know what would be best. Given the chickens' proclivity for digging, it seems that keeping some sort of cover is temporary at best.
Chris