Extract a javascript variable with flask
That doesn't make sense! 
Flask/Jinja can't read from javascript vars.
However, (as you said it is a POST request) you could:
Three ways:

Passing (dynamically modifying DOM link or form action URL) counter var value to POST request URL, like:
/path/postaction?counter=4;
If it's a POST request from form you could modify form action (see
above) or adding a input hidden to form;
Setting a cookie and get it in the next request (I don't like this option);
I am working on a little flask project and in my javascript script I have a variable which works as a counter. 
When I receive a POST request I would like my python script to extract this counter variable. 
I tried to set a jinja2 variable by doing {%set extractor_var = js_counter%} but it seems to be impossible to use a javascript variable inside a jinja2 template. 
Can anyone lead me to another solution?