The short answer: Yes, you should get him the flu shot. Every year. Because it's simply the right thing to do.
The other, non-influenza sicknesses he gets have nothing to do with the vaccine. The influenza vaccine is for influenza strains. That shot will ensure that he doesn't get the three most common strains of influenza for this season, and if he doesn't get them, he can't spread them.
The seasonal influenza vaccine protects against the three highest predicted strains for the year (as projected by the World Health Organization and CDC). They're very accurate projections.
Getting the shot isn't just about your son not getting sick (yes, he might still get sick with another strain, but it won't be the top 3)...it's about not SPREADING it to immuno-compromised folks who cannot AFFORD to contract it.
By getting your son and yourself immunized, you are protecting someone's premie, someone's grandma, someone's grandpa. In immunocompromised people, the flu often leads to pneumonia, which is all too often lethal.
Just something to consider. I hope you get your family immunized.
ETA: Also, if your son "gets sick all the time," please consider washing hands (his and yours) a whole lot more. And, if he's in daycare, consider talking to them about proper handwashing techniques. Washing should happen when they arrive in the morning, after toileting, before eating, each time they come inside the building from play, and before they leave for home each day. It seems like a lot, but consider all the things they touch and put in their mouths. Also consider buying a couple of cans of Lysol and disinfecting phones, door knobs, toilet and sink handles after he's in bed for the night.
Inadequate handwashing and not covering coughs and sneezes are a huge problem.
To the person above who complained about too many shots...Flumist is an excellent, non-needle option. Just a little squirt in each nostril. No needles and no pain. It even tastes a little sweet.
ETA 2: As a medical professional, this drives me nuts. "The flu shot protects you from LAST YEAR'S flu strain, not the strain that will be infecting people this year. "
Incorrect. The influenza vaccine protects against three PROJECTED strains of influenza. Those projections are scientifically calculated based upon WHO influenza maps and known mutations of the virus.
Also....GETTING THE FLU SHOT DOES NOT GIVE YOU THE FLU! While your body may show some signs of illness due to the natural immune response and manufacture of antibodies, you DO NOT have the flu.
Finally, just because you know someone who had an adverse reaction does not mean you will. Adverse reactions are VERY rare. They can be caused by allergies and recessive immune diseases. You MOST LIKELY do not have either of these.
Thank you for letting me vent. GET YOUR FLU SHOT!