It appears that he did have some interest in Egypt, although not of particularly long duration. The Oxford Dictionary of National Biography entry states that he was " ... a member of the short-lived Egyptian Society, which met in London between 1741 and 1743 ... " although this doesn't affect the fact that the medal bearing the legend SVA SIDERA NORVNT was probably made in Rome to commemorate Folkes' interest in Roman antiquities.
On the subject of Folkes membership of Masonic Lodges, it appears that he was a member of a Lodge that, ca. 1725, met at the (Duke of) Bedford's Head, Southampton Street (T. Stewart, English Speculative Freemasonry: Some possible origins, themes and developments. AQC 117, 2004; 116-183; p. 138 (Prestonian Lecture 2004), although Lane's has no mention of an actual Lodge of that name.
Also, I was still unable to find any results for London Lodge no. 78 that would fit in with the relevant dates.
However, a connection to Norwich, and Norwich Lodge no. 30 - presumably, the White Swan - has come to light, here (p. 193) and here (p. 388, n.2).
(More information on Martin Folkes here (578-593)).
Edited: insert missing word
Post Edited (18-Aug-13 17:44)