Starfleet is forbidden from having cloaked ships but are civilians forbidden from having one? It seems that a cloaked ship would be a great asset for say a smuggler. The tech seems to be widely understood so should be relatively easy to acquire.
We see very few civilian ships in the Federation. Mostly cargo ships. The criminal Harcourt Mudd manages to steal a couple of ships, whether they were private or Federation isn't clear (to me anyways). None of the private ships we learn about have cloaking tech that we are aware of.
Getting the Tech
Quark managed to acquire a damaged cloaking device on the black market. He ultimately gave it to some Cardassians in Profit and Loss. So there is opportunity for smugglers or a private party to acquire a cloaking device. In this particular case the item was illegal because the Bajoran government had made a law banning cloaking devices.
You could, in theory, acquire the technology from
the Aldeans, Suliban, Romulans, Klingons any of the races with the technology (How many Star Trek societies have cloaking technology?) or privately develop it.
The Treaty of Algeron, signed between the United Federation of Planets and the Romulan Star Empire, expressly prohibits the Federation to research, develop or use any sort of cloaking device.
It's not just StarFleet who cannot have cloaking technology, but the Federation as a whole. Thus Federation citizens are as forbidden to acquire and operate cloaking devices than StarFleet is.
Besides, it would make little sense that StarFleet couldn't have that kind of technology but civilians could. Even more so from an internal security point of view.
Of course, one can find cloaking device son the black market, but at great cost and risks. It is likely that the various security departments throughout the Federation keep a close eye on even rumours of someone selling or looking to buy a cloaking device, given what that technology can do and the potential consequences if the Romulans decides that it constitutes a breach of the Treaty.