It seems most information is anecdotal regarding Vitamin D and flu shots often helping to avert more severe symptoms. No surprise that there haven't been formal studies, given how new this virus is and how many larger Covid fires loom on the medical research horizon.
I get an annual flu shot because I've had the flu a couple of times in my life. Quite frankly, I've been to better parties and prefer to decline invitations to that particular one.
I take Vitamin D because about five years ago a blood test showed my levels to be low so my doctor recommended supplements.
Whether they help reduce Covid symptoms is anyone's guess, but I've seen no evidence suggesting they make it any worse.