The problem is that '_' underscores are not valid in header attribute. If removing the underscore is not an option you can add to the server block:
underscores_in_headers on;
This is basically a copy and paste from @kishorer747 comment on @Fleshgrinder answer, and solution is from: https://serverfault.com/questions/586970/nginx-is-not-forwarding-a-header-value-when-using-proxy-pass/586997#586997
I added it here as in my case the application behind nginx was working perfectly fine, but as soon ngix was between my flask app and the client, my flask app would not see the headers any longer. It was kind of time consuming to debug.