How do you pass variables using a HTTP post from a JS file/function to a separate python file/function hosted somewhere else?
You have to create some sort of communication channel between the javascript and python code. This could be anything, SOAP, HTTP, RPC, any number of and flavor of message queue.
If nothing like that is in place, it's quite the long way around.  A complex application might warrant you doing this, think micro services communicating across some sort of service bus.   It's a sound strategy and perhaps that's why your client is asking for it.
You already have Firebase, though! Firebase is a real-time database that already has many of the characteristics of a queue. The simplest and most idiomatic thing to do would be to let the python code be notified of changes by Firebase: Firebase as service bus is a nice strategy too!
I have JS running and essentially getting user entries from my HTML session storage and pushing these to a DB. I also need to use a HTTP request to pass a json object containing the entries to a python file hosted somewhere else. 
Does anyone have any idea of documentation I could look at, or perhaps how to get JSON objects from JS to Python. 
My client does not want me to grab the variables directly from the DB.