Next time you integrate young chicks, start much earlier with a panic room. That way you can achieve your goals in just a few weeks. Read my article in outdoor brooding linked below for how a panic room works.
Meanwhile, follow the advice of FlockMaster and start exposing the chicks to the older chickens immediately. The chicks need protection until they get to know and understand the temperaments of the individuals in their flock. That way, when you let them all mingle, the chicks will know who to trust and who they need to flee.
It really helps to have get-aways for the chicks to leap onto or run behind. Introduce some "furniture" into your run. Tree stumps, old chairs, and I recently found enormous value in an old card table.
One of the main concerns will be assuring the chicks aren't chased away from their food and making sure they get enough to eat to complete their development. That's where the card table comes in.
Normally, I keep chicks' food and water in their panic room, but yours are getting almost the size of the older chickens and a panic room isn't going to work for very long. If you place their food on top the card table, the chicks will find refuge there, as well as knowing they can eat in peace.
Other high perches will ensure the chicks safety since adult chickens may mostly shun high perches in the run during the daytime. After a week of keeping the two groups separate, I would let them begin to mingle with the precautions I've mentioned.
