It sounds as if those "berries" are hips.
You cannot grow a Knockout, like you purchased, from seed.
The seeds are the sum total of all the roses used as parents to produce that Knockout. This includes whatever parents of any other rose bush used way back to the beginning of the hybridization process of your Rainbow Knockout.
It's like us being the result of all our ancestors with none of us having identical DNA unless we happen to be identical twins.
Therefore, 100 seeds from the same plant and rose hip would result in 100 different looking rose bushes, with many of them having undesirable characteristics. No two would be the same. Some may be miniatures, hybrid teas, climbers, or a combination of all the above. They could be white, red. yellow, pink, etc. as long as a rose that color was used somewhere in the roses's lineage.
Any plant's ultimate job is to propagate, that is to produce seeds. Once they do that, they are done for the season. There is no need to bloom anymore. By deadheading, you remove the fertilized flowers and prevent the bush from making seeds. Deadheading results in the bush blooming again to make more seeds. Continually deadheading makes the bush keep on blooming.
Some roses set seeds easily while others do not. I keep the spent blooms off the bushes more for appearance than to promote more flowers.
In fall, along with the cooler temps, shorter days and the angle of the sun, leaving the hips on the bushes promotes dormancy for winter. It also provides food for overwintering birds.
At this time of the year, leave the hips on the bushes. I would think you can deadhead until the end of September in your area. After that leave the spent blooms on the bush to promote dormancy or at least a slow down of your bush.
It's fun to try growing roses from seed just to see what you get. Just don't expect a bush that looks like your Rainbow Knockout.
Once a bush with desirable traits is grown from a seed, the only way to propagate it is from cuttings or by budding (grafting)
Your Rainbow Knockout and all others sold are from one original plant and identical clones of that one plant.

Thank you Karl for all your help. I am going to leave well enough alone. I would think my Rainbow Knockout won't be doing much for a while. I do love my knockouts.