You might be able to do something if you create your own app and use it on your profile, but that's quite a bit of effort.
On a site like this it's trivial by simply embedding an image into your post, and then looking at the stats for that image. However, all the images you usually see on Facebook are hosted by Facebook...

_________________jonbwfc's law: "In any forum thread someone will, no matter what the subject, mention Firefly."
When you're feeling too silly for x404,
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