One option: Install 'Fing' (or some other network scanner) on your iPhone, put your Twine into Setup mode, connect your iPhone to the Twine setup network, then run a scan in Fing. The results will show the IP and Mac address.
Or...you can open up your Twine, remove the batteries, and remove the circuit board - the Mac address is printed on a sticker. (I'm not suggesting you do this.)
It would be really cool if a label with the MAC address were on the box, or if it were printed on the bit of the board the forms the battery compartment.
This for me was the only setback in an otherwise very slick and straightfoward setup procedure.
Answers
I found this other way to figure out Twine's MAC address (it works with a MacBook Air, by using the built-in airport utility to scan for network):
Open a terminal, an log as su
> ln -s /System/Library/PrivateFrameworks/Apple80211.framework/Versions/Current/Resources/airport /usr/sbin/airport
install the batteries and turn down Twine, run
> airport -s
(performs a wireless broadcast scan of nearby wireless devices)
Twine appears as:
\||| Twine 00:1d:c9:11:xx:xx -45 11 N -- NONE
Thus here there is the MAC address