Well depending on the circumstances you may be able to. A stolen t4i may not be worth it. But a 1dx may qualify for grand larceny and would depend on wether law enforcement wanted to be bothered.
Generally speaking, insure your equipment and replace it possibly with something better. If you find your camera online you can report it to your insurance company and let them deal with it.
As I understand, if someone were to be dumb enough to post images online that have the exif intact with a camera they stole, it would find the images.
However, camera thieves steal cameras to resell to a unsuspecting third party, who than may indeed post images taken proudly with his new camera.
However, there is little you can do to recover it.
There is a big jump between locating a photo taken with your equipment on Flickr, and finding the person with the camera and actually recovering it. Flickr is not going to give you the name and address of the member, they may not even know who he is, except that they do or should have a credit card number (maybe also stolen). It would take a police department or court order to get them to divulge that information. The person with the equipment may be accross the country from you, and you will have to either hire a attorney or travel to that location to file a complaint with the police. Then, good luck at having them do anything.
So, you may then have to pay thousands of dollars for a attorney and all the court orders, etc to try and get it back.
You have to be pretty lucky to get property given back to you without a hassle and expense. It does happen.
Pawn shops hold property for a period set by the local laws, and search for serial numbers of stolen property. As long as they carry out due dilligence, they will not be charged with being a fence, and the best and quickest way to get your property back is often to just to re-imburse them for what they paid.
If you go to the police, they may seize the item and put it in a property locker for a year or two until you get a court order to claim it.
Thats why I say that there is little chance of recovering it, you have to be pretty lucky, or you just go into paperwork hell.