Choke on finely chopped herbs. No. It doesn't work that way. Choking in something big is possible but unlikely. I know yours are just chicks so they don't need anything very big, but I've found peach or plum pits in gizzards of chickens I've butchered. Those are pretty big for a grown chicken.
What can happen if they eat long strands of vegetation is that a wad can form in their crop. Think long strands of grass getting twisted and wadded together into a clump. That wad can get so big it cannot pass out of the crop. That is called an impacted crop.
Another possibility is that long strands that make their way through the crop may wad up in their gizzard. Again, if it can't pass on through you have serious issues. Guess what, this is called an impacted gizzard. But if they have grit they can grind it up.
Don't let this frighten you, this almost never happens. About the only time you read about this on here someone gave their chickens a lot of long strands of grass in the run. People do that all of the time and it still almost never happens. But that is why some of us recommend of you give you chickens grass run it through the lawn mower twice so the strands are less than 2" long.
You are giving yours grit, which helps their gizzard. You are chopping small quantities of herbs into small pieces. I don't see that you have anything to worry about as far as choking.
Parsley and cilantro are fine. I grow those. When I'm cleaning out the garden my adults may get those, basil, oregano, chives, or thyme. I don't see anything wrong with giving them herbs but I don't see anything great about giving them either.