So you integrated a single chicken with a flock of three. Whether they are the home chicken or the chicken being added, integrating with a single chicken is often more challenging than if you have at least two in each group. Having two Silkies can possibly make it easier. What were the relative ages of the chickens when you integrated the one? More mature chickens can be pretty vicious to younger ones. Chickens can tell colors. It is possible the colors had something to do with it but it is also possible something else was going on. It is not always easy to tell what is really going on.
It sounds like you have successfully integrated a white chicken. If color had anything to do with it maybe since she is in the flock now the color of the Silkies won't be an issue. But Silkies do look different so appearance might make a difference.
So what would I do? The same as I do for any integration. As soon as possible, house the two across wire where the existing four can see them. My brooder is in the coop, my chicks go in there straight from the incubator so they essentially grow up with the flock. Not everybody can do that but I like to start the integration process as soon as I can. Mine start mingling with the rest of the flock at 5 weeks but you likely won't raise them that way.
How much room do you have, the more the better? When I let mine out they will probably get picked on by the adults when they invade the older chickens personal space. They quickly learn to avoid the adults and may form a sub-flock for several months, until they grow enough to be able to join the pecking order. So it is important that they have enough room to get away from and avoid the older.
The quality of your room matters. A run or coop where they cannot get out of sight of the older ones is not great unless it is huge. If you have something small like that you can improve it by adding "clutter". That means things they can hide under, behind, or even over the others. Since yours are Silkies that can't fly "over" might be hard. Widely separated feeding and watering stations can help a lot so the two can eat and drink without being bullied away. If your run is small that may mean one station inside the coop and one outside.
Try to not force them into small places with the adults. Try to give them enough room to get away. This is during the day and at night. Do not think that they have to sleep with the adults. They don't, not now. All that one big happy flock stuff can come later. When I'm integrating I don't care where they sleep as long as it is not in my nests and is someplace predator safe. When I'm integrating my only goal is that none get injured. It's that simple, no injuries. All that other stuff will come later.
Will this always work? No. We all have different chickens, each with their own personality. We have different set-ups, different amounts of room, different management techniques, lots of differences. But this is the way I'd try, regular chicks or Silkies, paying attention to what is going on and how they are behaving toward each other. Make your decisions on what you see.
