According to HofD he died in the "great sickness" Database: Biographical & Genealogical Master Index (BGMI)
19755
Allis, Samuel 1647-1691
The Cabinetmakers of America. Revised and corrected edition. By Ethel Hall Bjerkoe. Exton, PA: Schiffer, 1978. Originally published by Doubleday & Co., 1957. Biographies begin on page 19. (CabMA)
The Oxford Companion to the Decorative Arts. Edited by Harold Osborne. Oxford: Oxford University Press, Clarendon Press, 1975. (OxCDecA)