The latest version of the JuliaMono font (v0.042) has italic versions:
Some VSCode themes use italics as part of the highlighting, so the italic version of the current font will be used, if available (otherwise the current font will be mechanically obliqued). Here’s one theme which requests italic characters from JuliaMono for keywords and comments:
You can find the font on github at https://github.com/cormullion/juliamono. Please open issues there if you encounter problems…
I don’t use italics myself, so I don’t have many opinions about what they should look like. There’s some debate in type-design circles about how many of the non-letter characters should be italicized. For example, should the mathematical operators be italicised or not? For now, in JuliaMono the basic operators are italicized, the less common ones aren’t - a fairly arbitrary decision, I admit, which can be revisited one day. 
