There are three basic magnetic properties of materials: Ferromagnetic (magnetic) -- Paramagnetic. -- Diamagnetic (anti-magnetic)
Materials such as iron, cobalt, neodymium or nickel are ferromagnetic. The electrons in their atoms are arranged in such a way that they can be magnetized and will retain said magnetization under certain conditions, even outside the presence of other magnetic fields.
Materials like tungsten, cesium, aluminum and magnesium are paramagnetic. They will become temporary magnets but only in the presence of a (relatively) strong magnetic field. As soon as the external magnetic field is removed, they will return to their non-magnetic state.
Silver, copper and many other materials are diamagnetic. Not only are then non-magnetic, they are actually repelled by magnetic fields. If you put them in a strong enough magnetic field, it is possible to make small amounts of these materials levitate due to this repulsion.
Even though silver isn't magnetic, you might be able to detect an eddy current around it. Place it in a strong, alternating field and you can induce a field around it which can be detected with a second coil of wire. Metal detectors such as the ones you see in airports or like you see men using on the beach to find lost coins operate on the eddy current principle.
There are two coils of wire inside the detector head. One is the "exciter" coil. The other is the "sense" coil. The exciter has a fairly strong electric current going through it. This current causes an electromagnetic field to develop around the coil. Any metal which comes near the exciter coil will be induced to have its own temporary magnetic field. The sense coil is also induced to have a magnetic field but, when the metal comes near, the field in the sense coil will be partially or completely stifled due to the field around the detected object. The metal detector's electronics will sound the alarm when the sense field is interrupted.
It is possible to tell how much metal or what kind of metal is inside the detection field based on the strength of the response. Larger metal objects react more strongly. More distant objects do not react as strongly. Further, different types of metal exhibit unique characteristics inside the field. The induced field develops faster or collapses at different rates, depending on the type of metal. This is why security guards at airports are alerted when a person has a large amount of metal but not if there is merely a coin in his pocket. (The can set the sensitivity of the machine.) This is also how those coin finders on the beach can tell the difference between silver, copper and other metals. They detect the profile of the alternating field as it expands and collapses around the object.
So, no, you can not record information on a piece of silver-impregnated film but it MIGHT be possible to use eddy current detection to read information.
I am only supposing... It MIGHT be possible to "burn" a series of black and white stripes, similar to a bar code, on a strip of film and pass it through an eddy current detector. The alternating silver/clear patches on the film should be detectable. You'll have to experiment to see what you can do with this idea. I'm not sure how it will work. As I said, I'm just guessing.