Artifactory does not build Docker images. Although this functionality could be handy, it’s just not what a Binary Repository Manager does. That’s a CI server’s job. Artifactory is about state of the art managing the images (as, for example it manages jars and other binaries), and that’s a lot of work by itself (e.g. thing about complex A&A, locality, availability, promotions, supporting for every type of binaries you might need, etc.)
My recommendation would be using the right tool for the job, building the images in a CI server and managing them in the binary repository.
Here is an article on Artifactory Docker integration.
I am with JFrog, the company behind Bintray and Artifactory.