I agree. Don't worry about the oyster shells. The young ones may experiment a bit with them but they won't eat enough to do themselves any damage. Just offer it on the side.
Sometimes integration goes so smoothly you wonder what all the worry was about and sometimes it is pretty rough. And we do it at all dfferent ages. I usually have mine running around with the main flock by the time they are 8 weeks old. I'd do it sooner but I like them to get a bit of size on them so they are not such hawk attractors since mine free range. I know. I'm being over-protective, but that is just me. A broody hen may wean her chicks at 4 weeks and those chicks are part of the flock, fully integrated. At 14 weeks age, you can certainly start.
There are two types of aggression you need to be aware of. You don't have roosters so you don't need to worry about the third. The first one is pure integration. If the other chickens don't accept the new chickens as members of the flock, they may try to run the intruders out of their territory. Some may even hunt them down to destroy them. Usually this is a hen when you have one of these seek and destroy chickens, but it can be a rooster. And many flocks do not have chickens that do this. One way to help this situation is to house the new chickens within sight of the flock for a week or so. If you can partition off part of your coop or move a cage or dog crate in there, that might work. It is not always easy.
The other aggression is the pecking order. Each and every chicken has to know its social standing within the flock. Knowing which ones are superior socially is how the flock manages to live close together fairly peacefully, but sometimes it is not very peaceful determining that pecking order. Sometimes that pecking order is determined more by intimidation than physical violence, but it does very often involve pecking.
Immature chickens are socially inferior to mature chickens. It is perfectly acceptable, according to chicken etiquette, for a higher ranking chicken to peck a social inferior if their private space is invaded. As long as the inferior runs away and acknowledges the others social superiority, the pecking order has been maintained and things are peaceful in the flock again. If the inferior does not run away, then it is seen as a challenge to the pecking order and violence may follow. That's why they need sufficient room to be able to run away. In integration, just like regular flock life, space is your best friend.
Since the immature chickens are automatically socially inferior, they will normally try to stay away from the older chickens. I suggest extra feeders and waterers to reduce possible areas of conflict. And as much space as possible for them to get away and stay away. Even different sleeping areas for a while can help, until they really get used to each other. My current group of 9 week olds still sleep in their grow out brooder instead of the main coop. My situation may be different to yours since mine free range, but I find the worst aggression is on the roosts.
One story that may help illustrate this. My broodies raise their chicks with the flock. I've seen 2 week old chicks stand next to other adult hens and eat out of the same feeder. Sometimes the other adults ignore the chick, but usually one will eventually give that chick a peck, reminding it that is bad chicken etiquette to eat with your social superiors. The chick goes running/flying back to Mama as fast as it can, peeping the whole way. Mama ignores this. Sometimes it takes a flock to teach chicken etiquette. But if that hen were to really go after the young chick and try to hurt it, Mama would be all over her, protecting her chick.
Each chicken has its own personality and each flock has its own dynamics. We all have different goals, situations, and management styles. I can't tell you what will happen when you try to integrate, but do think it is time you started letting them get used to each other.
Good luck!
