To get a development installation of Flit itself:
git clone https://github.com/pypa/flit.git
python3 -m pip install docutils requests
This links Flit into the current Python environment, so you can make changes and try them without having to reinstall each time.
To run the tests in separate environments for each available Python version:
tox has many options.
To run the tests in your current environment, run: