Yeah, I'm not satisfied with that answer either, yet it's the official one, and it seems like there's no other option.
I'd have a button to report a false duplicate flag, but if everyone ends up spamming it, then what's the point of the automated approval? Because it was implemented to reduce the load on emotes approvers. There could be repercussions for the people abusing it tho', just like there is for people abusing the report system.
Here's what I'm suggesting to try for now:
1. click on View Original Emote
2. if it's clearly different than the one you're trying to upload, then click on Report Emote
3. select In the emote's image content, click Next
4. select Something else, click Next
5. explain your issue, upload the emote you can't add to an image hosting service (such as Imgur for example) and share it with them so they can see it's a false flag, and hopefully they can help