I do not know specifically if the vaccine can raise his BG. It can certainly create inflammation and that in theory can affect BG.
Why did your kitty have a Leukemia vaccine? Is he at risk of contracting Leukemia? Is he an outdoor cat ? Is he exposed to other cats who may bite him? The feline Leukemia vaccine carries significant risk. There is a risk of malignant sarcomas at the injection site. I have a friend whose cat passed away from one. Now I had a cat who was vaccinated with the Leukemia vaccine before I was aware of what the vet was doing (many years ago). She had some bad side effects but luckily no Sarcoma. I’m only mentioning this now because you may not want to get this vaccine for your dear kitty again. It is not one of the core vaccines for cats.