The REST API that I'm using allows me to authenticate with an HTTP action, but it returns a cookie that then needs to get passed to the next HTTP action if I want to actually do anything with the REST API.
It was working by passing the HTTP Headers Outputs from the first HTTP action to the HTTP Headers Inputs of the second HTTP action. But now something changed in Flow to break it.
I guess what is really needed is official support of cookies between HTTP Actions in Flow so we could pass "state" between two separate REST API calls and this scenario would be supported.
Here is a discussion thread on the specific scenario that I'm working with (click here).