If you are wanting to run the chickens behind the cattle as "fly control" then you need for the cow to be ahead of the chickens 48 hours or more. Depending on the weather and such. Most that I have heard and done is about 3-4 days behind the cows. Research the life cycle of the flies that are your biggest problem and follow with the chickens accordingly. Once you get the fly population down, then being with them or near them will keep the manure piles spread out and the flies will not have many places to lay the eggs and there will be little larvae hatching for them to eat. If you want them to simply free range and eat the bugs in general, then they can run together. One thing, if the chickens have lice, the cows can get it from them. Lice can be a "multi-species" pest as opposed to some things being species specific. On pasture it isn't much of a problem, but chickens in the same barn can be.
One thing, if you are thinking something like a mobile chicken coop then I would run them in a separate field. One thing that we found is that the cows will be trying to get into the coops for the feed, and they will try to get their heads in the little "trap door" that the chickens come out and can start to tear it up. They will also try to get to where they can reach in and eat the poultry manure if the birds have a roost pole(s) for night time roosting. We used smaller camper trailers and retrofitted them for the chickens as mobile coops for about 100 birds in each. Feed and water in the coops, roosting poles for the night. I let them out free range days, then locked them in at night. The cows would practically stand on their heads thinking there was something in there that they needed to have to eat, trying to reach in the little trap doors. If I opened the big door in the summer, I had 2 2x4 "bars across the doorway so the cows couldn't go in. And yes, had calves that would hop up in there. This is FUN!!!!! But they would reach their heads in there, try to get into the feeders, knock the 5 gal automatic water fountains over, and try to get whatever they thought they ought to have. And I am talking summertime, with pasture up to their knees. PITA nosy cows!!!!