Do you mind very much if I ask a few questions? There are some things here I would need to know in order to help. For example:
are the shots prescribed by their vet
how often is kitty getting them
by vit B shots are you talking about a combination of different B vitamins or
B 12 shots
has your friend discussed this problem with their vet
does this kitty have IBD or CRF
what else is kitty being treated with for any other kind of health problem; anything at all, supplements and medications
what is kitty's diet; what kind of food (canned or dry); what are the ingredients
To explain, just recently I had reason to look for every piece of info one could possibly find on the side effects of B vit shots, specifically B 12 shots. There is a long list. But, if dental decay is a possible side effect, I didn't see it anywhere. Which doesn't mean anything, of course. I'm just saying, I didn't see it.
What I do know is that different B vitamins have a different effect on pH. Some have an acidifying effect, some have an alkalinizing effect. They can affect the pH of the saliva, and possibly the urine pH as well. Changes to very acid or very alkaline can affect the tissues of the mouth, even cause severe inflammation. (I have experience with such inflammation.) So I imagine it's not impossible that long-term, such changes can also affect the teeth.
Talking about dental decay, I'd just like to mention very quickly that lack of vit D has been linked to dental problems, so I'm wondering if this kitty is getting the proper amount of vit D in the daily diet.
As for the B vit shots, this is something your friend definitely has to discuss with their vet. I would urge your friend to have saliva pH and urine pH tested. In my mind complete blood work and urinalysis are in order, and diet also needs to be discussed with their vet.
Sometimes problems can arise from the best medications or supplements, so it's possible that after a very thorough vet check your friend will need a lot more help from their vet. They will probably have to try and experiment with different things, including kitty's food. Would you know whether the underlying cause of the vomiting has ever been determined?