I'm sure I had this working on another laptop, but I have an issue on this, the left alt-key somehow doesn't work for user applications (window manager, etc. no problem, haven't fixed it yet), but no problem, I tried to reconfigure it:
Ctrl+Shift+D - Well, that just opened "add bookmark" popup - that was warned against though, not being able to override browser bindings.
Then I tried pretty much any Ctrl+Shift+[key] - none worked.
Btw, I tried Ctrl+Shift+. and worder if with shift key in the mix I should try ':' and not '.'.

So the issue is, this is useless. I have another add-on, Saka Key, which is really for full keyboard browsing, but the tab tublicate on it doesn't work the way I want with Tree Style Tab. Maybe yours would...?

As of it now, it just seems it only works with Alt, not with Ctrl. Either that or something in my FireFox is messing with it. At the moment it is useless on my main PC :(

Just got it, changed shortcut, tested it, it works. Yay!

1/10/2020 Update
It stopped working a few months ago. Don't know if there was a FF update. All it does now is open a new tab, no duplication. Using FF 72.0.1 in LinuxMint.

Not working with firefox 59

Very unreliable - works once then fails in Firefox

Duplicate tab is an essential feature Mozilla!

Very unstable. Does not work most of the time.

Doesn't work in the German version. It opens the file menu with the shortcut alt-shift-d. No, I don't want to fix it in the source code.

If keyboard tools don't take care of international versions of the software they are ment for, then they don't deserve a good rating. Alt-Shift-D will trigger the file menu in a German Firefox. Does not work.