The spelling of Zink for Zinc has been followed up on at the English Language & Usage Stack Exchange as Was Zink ever valid spelling for Zinc? where the earliest known spelling of Zinc is from 1813.
With Thomas (born 1797) presumably going to school before that, and becoming a school master less than 10 years after 1813 (certainly by 1821, and finishing in or soon after 1827) it seems unsurprising that he continued spelling it Zink which was probably what he was taught and what he taught.