Galloway was born in Oakland, California, and received his B.A., C.Phil., and Ph.D. in linguistics at the University of California, Berkeley, in 1965, 1971, and 1977, respectively. He has done linguistic field work with the Haisla language, Upriver Halkomelem (from 1970), Nooksack (from 1974), the Samish dialect of Northern Straits Salish (from 1984), and Gullah (from 1994). In the case of Nooksack and Samish, he worked with the last surviving fluent speakers known then (one speaker has become a fluent speaker of Nooksack since 2002, and there may be 3 or 4 descendants who speak Samish).
From 1975 and 1980 he founded and headed the Halkomelem Language Program at the Coqualeetza Education Training Centre in Sardis, British Columbia. He there developed the Stó:lō Halkomelem orthography which was subsequently adopted officially and is now in wide use throughout the Fraser Valley. He also compiled the first grammar of Upriver Halkomelem, published in 1977, plus treatises on the region's ethnobotany and ethnozoology. According to Galloway, some words in Halkomelem "encapsulate the whole knowledge of the culture." The language has a rich oral literature which shows a whole way of looking at the universe that is different from that of English or other European languages.
In 1988 he joined the Saskatchewan Indian Federated College's Department of Indian Languages, Literatures, & Linguistics and served as its head from 1988 to 1994. He continued to work extensively with Halkomelem and Nooksack language education and completed dictionaries for Upriver Halkomelem (in press with University of California Publications in Linguistics. 2 vols.) and Gullah (co-authored with Virginia Geraty), "A Phonology, Morphology, and Classified Word List for the Samish Dialect of Straits Salish (1990 National Museum of Civilization, Canadian Ethnology Service, Mercury Series Paper #116), a "Grammatical Sketch and Classified Word List of Upriver Halkomelem" (1980, Coqualeetza Education Training Centre), a "Classified Word List of the Nooksack Language" (co-authored with George Adams, 2008), Nooksack Place Names (coauthored with Allan Richardson; published by University of British Columbia Press in 2011), and about 100 descriptive articles and papers Halkomelem and Nooksack and several on Assiniboine and Samish. As of October 2008 he was working to complete a Nooksack dictionary. His work on these languages was based on original field work and recorded tapes now on CD.
Galloway also wrote a number of papers and articles on his theory of cognitive semantics, first called Three-Dimensional Semantics and now called Multi-Dimensional Semantics. He retired in August 2008 from First Nations University of Canada and was appointed Professor Emeritus there, a position he held until his death six years later.
Dr. Galloway was also a composer of classical music (since 1956, mainly piano pieces, then synthesizer and orchestrated pieces). His orchestral pieces The Night Before Christmas and Mexican Colors have been performed by the Regina Symphony Orchestra.