Cloning repository and installing dev dependencies:

git clone https://github.com/gustavjf/flycheck-issue-repro.git

cd flycheck-issue-repro

yarn

Reproduction:

At this point, you should be able to open index.js inside emacs and run C-c ! v to inspect the current flycheck status and see the ESLint errors highlighted in the buffer.

Now, try initializing the flowtype config by running yarn flow init.

Notice after .flowconfig is created that when you return to the buffer and make changes, ESLint errors no longer appear - only flowtype errors.

When you remove .flowconfig, the ESlint errors are now visible again, and as expected, flowtype errors are not.