hey tony, welcome to the forum, the best source of material for making a balearic sling is to use good quality sisal string; its a light creamy white from personal experience, and is composed of the fibres from the agave sisiliana plant, which i've found to be the most associated plant to use when making the balearic slings, however, a lot of other stuff may be substitued, that may range from any fibrous material (i've used a lot of hemp string to make a few) to cotton.
also, balearics are often made in five plait, instead of three, its not very complicated, they're actually both quite similar, however i recomend that you read some of the posts from this site:
http://www.seekyee.com/Slings/howtos.htm just go to the 5 strand braid section.
also, heres a post that i began that has some good info in it;
http://slinging.org/forum/YaBB.pl?num=1301613713/0i hope you can find something informative in the vastness of interweb space. good luck.
the dog