Hi and welcome to the forum 🙂
It's certainly possible that the flu vaccination is messing with his levels. The nasal spray contains a live (weakened) form of the flu virus, so your son's immune system may be dealing with that! Not everyone reacts to it in the same way though - my son didn't have any noticeable effect on his BGs this year.
It's always possible of course that there could be another reason for the turbulent levels, e.g. he could be having a growth spurt or incubating some other illness. You just have to go with the numbers and adjust his insulin accordingly. Is he on MDI (basal-bolus)? Has your clinic team taught you how to make changes to his insulin doses?