You can pipe the diff into specific flake8 checkers. Disable the check by default so it's not run over the entire codebase, and have a separate line for running specific checks on just the diff. Eg:

git diff -U0 --relative origin/master... | flake8 --diff --select <custom-codes>

I'll leave the flake8 plugin as an exercise to the reader as ours is intertwined with code I can't share right now.