"Probably as much interest is taken in the famous "three-legs sign" as in any feature of Manx archaeology. It is a constant cause of enquiry... The question cannot be definitely answered, though there are two strong and interesting theories, merely differing in their explanations in the matter of date, because both theories trace back the history of the "three legs" to Sicily. There is no doubt that the three legs were famous in Sicily as a badge, from very early times. ... a vase from Agrigentum, Sicily ... is an early fifth-century B.C. specimen, depicting ... a fierce fight between Achilles and Memnon (in error named Hector)... Memnon's shield bears very boldly depicted the trinacria, now so familiarly associated with Mann.

... it is generally considered to have been derived from the "fylfot" or "swastika." In its four-legged form it is one of the most ancient decorative devices, and was in use as the badge in India of the opponents of Brahminism, the "Swastikas" (hence its name). It was seen in Greece as an ornamental device, in Rome on many alters, and in Scandinavia as a representation of Thor's hammer or "thunder-bolt." As such it appears on Scandinavian crosses in the Island. It is not know how the number of arms came to be reduced from four to three. But, undoubtedly, the Sicilian device was booted, and the feet were running in a clockwise direction. In the vase-representation above mentioned, the feet were not spurred. ...

The vexed part of the question is (a) how did the sign come from Sicily to Mann, and (b) when did Mann adopt the sign? Of two possible answers... one suggests that it probably came by and through the Scandinavian Kings of Mann, 1079-1265. The other, that it came through Alexander III of Scotland, to whom the Island was ceded in 1266. The Scandinavian kings had well-known connections with Sicily. ... Alexander III ... attended the English court where preparations were being made to enforce the claims of Henry III's son Edmund as King of Sicily. ... at the English court the Sicilian badge was a very familiar and prominent device. Later, when Alexander came into possession of a similar "island kingdom," he adopted the badge of the "island kingdom." Stenning

Sources:
Isle of Man, Canon E. H. Stenning.

http://www.montaguemillennium.com/familyresearch/mann.htm