I had the problem, that Skype for Linux wouldn’t open links in Firefox but a different installed browser.
BROWSER=firefox didn’t solve the issue.
The solution was to tell xdg-mime the proper app for
x-scheme-handler/http mime type:
Edit in your home directory the file
~/.local/share//applications/mimeapps.list and add:
Now Skype opens all links in Firefox (iceweasel in Debian).