If I run an app in a docker container using Kitematic, does that help protect my system from that app?
I mean: does it prevent any problems if the app tries to damage the Operating System?
Whilst no single layer of security can provide complete protection from attack, adding a layer of containerization/virtualization to a solution adds a barrier which an attacker would have to overcome to attack the host system.
In the case of Docker on Windows (so running linux programs on a windows host), it makes use of Hyper-V virtualization so an attacker, to successfully compromise the application, would have to break out of both the container and the Hyper-V VM to compromise the underlying host.
Even with an additional Security Layer like Virtualization/Containerization, you are running this code at your system. If there is faulty code in this implementation, Docker in this case, the application will break out of the container and execute code at your host os.
Docker CVEs from the past: https://www.docker.com/docker-cve-database