It's common to give several vaccinations at one visit. The MMR and Chicken pox are live vaccines and must be given on the same day or separated by 30 days. They are given subcutaneously. The flu shot in an inactivated vaccine and is given intramuscularly. It would be a good idea to wait until he is completely well to get any vaccinations
Given your son had a reaction to the previous flu shot, I would avoid giving him additional flu shots. Flu shots are not necessary. Vit C, vit D and good hygiene are more important.
Even if you decide to do flu shot, do it separately from the MMR, and chickenpox. Don't do any shots while he is sick.
Better to spread out shots anyways so to reduce the stimulation to his immune system. Be very careful with vaccination.
You can go to Mercola's web site (type Dr Mercola and 'flu vaccine' into your browser) if you want to read more about flu vaccination and flu prevention.
Best wishes