I've never connected Flow to webpack or my compile process like that. When I've used Flow or TypeScript with Babel, the build process and type checking were always two separate things. I treated type checking like unit tests: something I'd frequently re-check while working on code, but not something connected to the path of getting code running somewhere.
Not necessarily locally. On CI/staging/prod yeah definitely, but when I'm hacking around I'm fine with having type errors ("yeah yeah I know this is nullable, I don't care right now I just want to investigate this bug")
I absolutely want it locally, preferably inside my IDE where it's providing type hints, allowing navigation to type declarations, and alerting me immediately to typing issues live as I'm coding.
I don't really feel strongly about it, though sometimes Flow takes 10+ seconds to re-check a large project I work on after changes, and I wouldn't want building to have to wait on that. (I've never worked on a similarly-sized project in TypeScript, but I expect it's about the same situation.) I usually use a CI system (CircleCI) which sends me an email if any of my commits don't pass type checking or unit tests, and it flags any PRs on Github that fail too.