I have the very same issue here and I can't get the powerline fonts working on VS code with ubuntu.
Try setting: "terminal.integrated.fontFamily": "monospace",
still not working...
Edited: My Solution.
instead of moving the font file to hidden folder .fonts in user home do this in ubuntu
sudo mv Menlo\ for\ Powerline.ttf /usr/share/fonts/
then sudo fc-cache -vf /usr/share/fonts/
I'm using ubuntu 18.04 at the moment of writting this, hope it helps.
Works for Fedora 30 as well!. Tnx.
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