Won't this (having a flu vaccine every year) put them in an uncharted territory as far as effects on the immune systems are concerned within a couple of decades?
You are exposed to and develop a memory response to many, many more pathogens than vaccines. Your collective immune memory from natural exposure to a pathogen is much, much larger than from vaccination.
Effective vaccines reproduce the immune response of exposure to a pathogen (see the CDC pink book, Chapter 1). Some use specific subgroups of antigens important for protective immunity, some use killed viruses that don't replicate in the host, and others use live attenuated viruses that replicate, but don't cause disease. The number of vaccines you get is much smaller than the number of different antigens you are exposed to. Considering the common cold alone, the incidence in the US is 6 per person year for children, 2 per person year for adults without exposure to children (see Cecil Medicine Ch. 369). Each of these exposures involves many different antigens. Vaccine related immune memory is a drop in the bucket.
Beyond this, the basic premise (that you have a small amount of immune memory storage relative to the number of vaccines you receive) is wrong. There are over 3 billion B-cells in your body at any given time, with about 100 million different B cell receptors. This repertoire of antigen receptors is enough to match every single (or nearly every single, depending on who you ask) possible macromolecular antigen. For a protein, or protein conjugated antigen, the product of that match can produce long lived high affinity memory B cells, and long lived high affinity plasma cells. Your immune system has the memory capacity to deal with a great deal more antigens than the number of vaccines. You can read about these basic immunology details in Sompayrac's How the Immune System Works (Chapter 1 gives the numbers I've discussed here, and discusses how the repertoire of antigen receptors matches up with the number of possible antigens). Other basic immunology texts (e.g., Abbas, Janeway) cover the same, but can be a little more dense.