Perhaps another clue what the brass/steel clips were, is referenced in Bob Hunts book "Randall Military Models Fighters, Bowie's and Full Tang Knives, page 286-87.
Bo refers to it as "bent brass with hole drilled". No mention of chain. Hole drilled would seem to indicate a round hole as the example in Pete Hamilton's book.
Also in Robert Hunts books, when describing this wrist thong holder, always refers to it as a clip.
Not quite sure where the term "chain link" comes from, but I don't think they were taken from a furnace chain.
I agree with Bill too. Referring to these historic early Randall Fighters as a "chain link fighter" is wrong in many ways. The word chain has no place in the description, IMO.
Regards, Sam