As far as exhausting junk/grass/branches, this is either on a long timer or more likely is reset when the server is reset (like when animals respawn, not after a minor crash).
Resources like the available junk types and rare spawns like flint/chalk/shells are on a timer, but taking a resource also has an effect. There have been times when I've gathered flint right after it popped up and then a quartz appeared, or a shell appeared and another shell popped right after it was gathered. Chalk does not show up over as wide an area as flint/quartz. Often a single step will take you past the chalk spawn, so gathering limestone may be a more reliable method than walking if your reflexes aren't sharp.
Ravelli
For me the gathering stone method is simpy a way to multi-task. I would grind tools with the stone and when/if the rare pops up I'd grab it. That way I'm not just staring at the screen for 20 minutes waiting for chalk.