Welcome to the group, as @SueMartin said we are happy to share our thoughts and experiences, but medication is always a personal decision after having taken advice from Neuro, PD Nurse and or GP.
In my honest opinion, I have been having the flu jab for about 14 years long before dx with parky. The reason I decided to have it is I caught flu in 2005 and was so ill with it I could not keep my medication for spinal stenosis and osteoarthritis down for about 5 days which made everything worse I my honest opinion.
Since 2006 I have had the flu jab every year, only side effect I have had and not everytime, is a sore arm and a slight headache. I have not since 2005 had flu, a heavy cold yes (but it is not designed to prevent that).
For me personally I will be having the flu jab again this year and have my appointment booked free via Boots on 18th September as it means I get it a lot sooner than if I wait for my appointment with the GP surgery.
I hope you find this helpful