Normally when you run Chocolatey to install a package, you should run your Terminal as Administrator.
Fire up the Termimal and use Chocolatey to install Python 2.
Python 3 will currently not work when initializing a React Native project.
Fire up the Termimal and use Chocolatey to install NodeJS.
The React Native command line tools allow you to easily create and initialize projects, etc.
If you see the error,
EACCES: permission denied, please run the command:
sudo npm install -g react-native-cli.