I have had an opportunity to examine the Petrie museum sling up-close and personal. The photo at the top of this thread is one of mine. I have many notes and extra photos, so I may be able to help you further. I intend to attempt my own reconstruction just as soon as I can find the time! All I have so far is a few trial pieces. The original is beautifully made.
The sling was reconstructed by Burgess way back in the 50's. His reconstruction is also at the museum - it appears in some of my photos in the gallery here:
http://www.slinging.org/gallery2.html These photos don't show the finger loop clearly. I have found reproducing the finger loop particularly tricky.
Burgess' very detailed paper was published here:
Burgess, EM 1958 An Ancient Egyptian Sling Reconstructed.
Journal of the Arms and Armour Society 2.10 June: 226-30.
With a supplementary note here:
King, F H 1960 A Note on The Square Sinnet,
Journal of the Arms and Armour Society 3.7 September: 187
You can get these from the British Library for a small fee.
The sling has also been reconstructed by Thom Richardson. The following article discusses his experiences:
The Ballistics of The Sling, Thom Richardson,
Royal Armouries Yearbook, Vol 3, 1998. pp44-49.
You can get this book from the Royal Armouries, Leeds, UK. See here:
http://www.armouries.org.uk/ There is a shop and a photocopying service.
The text of Richarsons article appears here:
http://www.slinging.org/25.htmlI have not checked to see how complete this version is, but I see that Richardson's pictures have been replaced by mine!
The sling is almost certainly flax (I said in another thread that it was hemp but that was not right, although hemp would produce a very similar result). The braiding of the arms is a 12-strand eliptical sinnet with some fancy work for the finger loop. The end of the other arm is missing. The cradle seems to have been woven rather braided, Burgess made a diamond shape loom (which also appears in some photos). Although the loom is speculative, the resulting reconstruction is indeed very much like the original.
For more help and/or exchange of information, please contact me directly.