Can dosing vancomycin too fast cause renal failure?

Usually not. It causes flushing and not feeling well. However, if someone allergic to any drug he/she could develop renal failure.
Vancomycin dosing. The keys to your question are 3 - what was renal function before giving the vancomycin, what was the blood level of drug after dosing, and how many doses were given? Kidneys are damaged when vancoymcin levels are high and these factors are all important to really comprehend fully your question.