Flu shot at home ?

Check with your local health department and/or Social Services. Some areas can send out a Public Health nurse for inoculations.

Visiting nurses can do them where I live in upstate PA. Just call and schedule. They will call PCP to get authorized.

Call your Area on Aging and inquire about Community based solutions. It may be difficult to get it in your home but not impossible.
There may be states that allow MA’s (medical assistance) to give flu shots, maybe the MA can do it.

I think that the advice below is great. Do check with his doctor. And if he has to leave for ANY reason in the next month or so a trip to most drug stores will get him a flu shot, as well. If he is fairly homebound now do call and see how he can get his shot. Do know also, that if YOU and his other visitors are protected from the flu he, being homebound and not exposed to a whole lot of germs lessens his chances a bit. Still safest to do the preventative care of the pneumonia and flu shots.

Heal.com is a service is some bigger cities that provides house visits from doctors, including flu shots. If you're not in their service area, perhaps you can find something similar. In California nursing services have difficulty providing home visit flu shots because they require the cooperation of a doctor to provide the shot, which they are often reluctant to do.

Call your Drs office and see if they know a service. Is there a Visiting Nurse Assoc? See if they can help. Ask a pharmacy.