What might "three several" mean?

Although you don't hear it much at all these days, several used to have the additional meaning of distinct or separate. It probably just means "three individual fires" in your example, as distinct from three things being burnt in one larger fire.

From TheFreeOnlineDictionary:

several adj.
2. Single; distinct: "Pshaw! said I, with an air of carelessness, three several times" (Laurence Sterne).

The dictionary entry for several lists the following as one of the definitions:

Single; distinct: "Pshaw! said I, with an air of carelessness, three several times" (Laurence Sterne).

So in this case several doesn't mean a relative number (like a few), but instead that there were three distinct fires.

This unusual definition is related to the etymology of "several":

early 15c., "existing apart," from Anglo-Fr. several, from M.Fr. seperalis "separate," from L. separe (ablative of *separ "distinct"), back formation from separare "to separate" (see separate). Meaning "various, diverse, different" is attested from c.1500; that of "more than one" is from 1530s, originally in legal use.

The other contributors are correct. Several here means separate or distinct.

There is one place that I know of that this usage is still common, and that is in the legal term "joint and several liability." This means that if two or more people enter into a contract together that they are liable for the obligations both as a group, and also as distinct individuals.