Realistic chemical spill accident in high school chemistry class
Collecting together the responses from the comments and Ben Norris's answer and adding one of my own, individual solutions in water of the following chemicals are realistic options for a liquid spill in a high school chemistry lab, leading to destroyed clothes and time under a safety shower:


Potassium permanganate $(\ce{KMnO4})$
Sulfuric acid $(\ce{H2SO4})$
Hydrochloric acid $(\ce{HCl})$
Nitric acid $(\ce{HNO3})$
Sodium hydroxide $(\ce{NaOH})$


As for an experiment leading to a spill, one possible example would be in the course of filling a buret in preparation for a titration. Burets are usually quite tall and narrow (click image for larger version):

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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(Marketing image from Microtech Scientific)

A slip while filling one could easily result in spilling a few hundred milliliters or more of liquid on oneself.