There is very little evidence of deaths caused by vaccines (unless you buy into the myocarditis stuff with COVID19 vaccines), but there is a causal relationship between certain vaccines and Guillen-Barre Syndrome. It is about 4.9-5.9 cases per 1M vaccination doses, and between 3 and 13% of people with GBS end up dying from respiratory failure, heart failure, and other autonomic system failure.

If you extrapolate numbers, that is about 200 kids per year who will get GBS from vaccinations and about 6-26 who will die from it.