I am trying to push the tests to TFS and it asks for the Platform and Flavor on the TFS Publishing part of ArtOfTest.Runner.exe.
Did you mean you're trying to push the test results to TFS? Pushing tests to TFS means you're trying to put them into source control and source control doesn't have the concept of platform or flavor.
When you push results to TFS they are associated with a specific TFS build. So you have to look up a build in TFS in which to connect the results too. If there is no TFS build to associate the results with then you cannot do a push. Usually you're trying to associate the results with a specific build of your product. I suggest you get in touch with your developers and see how your product is being built and if there is a TFS build in which you can associate test results with. They can help you in identifying the platform and flavor of the build.
Regarding putting tests into source control in TFS when you connect a Test Studio project to TFS you choose which folder in the TFS source control tree where you want your test project to be added to. This is documented on our page Connect Project to TFS