Uncovering Secrets Framed in Gold is tracked as a quality, not as an item. Specifically, you can find it under the Intrigue category of qualities on your character page; the non-item qualities are on the bottom-left. You can raise this quality, but it indicates that you've explored the secrets of the painting further, not that you have additional paintings. (That's why it's tracked as a quality rather than as an item. And if I want to get really pedantic, all items are treated by the StoryNexus engine that powers Fallen London as Qualities, but that's irrelevant.)
You picked up your first point of USFiG from an opportunity card called A Bewildering Salon, which is only available once you become a Scholar of the Correspondence. You will gain more of that quality from opportunity cards. This storyline is, unfortunately, one that costs a little money to complete; the wiki says it takes 19 Fate/Nex. (I believe that's either all of or more than the amount of Fate you can pick up normally in the course of playing the game.) As with all storylets that cost Fate/Nex, it rewards you much better than storylets that don't cost Fate/Nex.
This particular storylet occurs entirely in opportunity cards; at every stage, the next step is to wait for another opportunity card. Yes, this takes a while. (My current USFiG quality, now that I've completed the storyline, is at 55, but that's misleading because USFiG occasionally jumps upward by a large amount when you take certain actions. I'm fairly certain there are multiple end-points of the story, with different values of USFiG.)