You can set a package in your channel to private by, first, navigating to your profile on Anaconda Cloud and clicking "View All" in the Packages pane. You can also get there by navigating to https://anaconda.org/username/repo.
Click on the package that you'd like to set to private. This will take you to https://anaconda.org/username/package. Click on the Settings tab and then click the Admin tab.
Here you can select either Private or Authenticated. Once you select either of these options you will have
the option to save your change.
Your package is now private.