Double Insulation as I understand it to be, means that there are 2 layers of insulation between the live part and surfaces which are normally touched by the user of an appliance, etc. The same goes for flex's, although for some odd reason, TV's and the like only use cords with single insulation.
Most of our light-duty appliances (TVs, radios, record players, fans) used to come fitted with 18-gauge SPT-1 cord.
In the past couple of decades there was a movement to equip things like TV sets, some hi-fi equipment, blenders, etc. with 18-gague SPT-2 cords. SPT-2 has thicker insulation. SPT-3 is the thickest you can get for parallel cord (at least that I've seen). SPT-3 is normally used for air conditioner extension cords -- normally they're built using 14-gauge wire.
Anyway....in the past - oh I'd say - five or six years, almost all UL-Listed electronic equipment (TVs, radios, tape recorders, turntables) started coming with the following:
NISPT-2 at 18AWG.
I think UL has been one of the ones reponsible for this -- the reason being the insulation is thicker, and less prone to getting nicked. UL-Listed fans and lamps are now being sold with 18AWG/SPT-2 cordage. The fans have had it for years. The lamps, only in the past two or three years or so.
The "NI" stands for Non-Integral. In other words, this is essentially flat SPT-2 cable that is encased in a tough, abrasion resistant thermoplastic jacket. Construction is similar to the thinner European version.
There are also some replacement cord-sets sold for cassette recorders that use NISPT-1 18AWG cord and some no-name cordsets that are actually made with .75 mm harmonized cordage (also double insulated).
Unfortunately, you can't buy NISPT cord in bulk at your local hardware store to replace the cord on your TV set that your dog chewed up.
SPT-2 cord in 18-gague is also pretty difficult to find in bulk. Certain mail-order places, however sell 18AWG/SPT-2 ready-made cordsets with moulded plugs (for replacement use or OEM)
If you're buying bulk zip-cord off the spool in most hardware stores and lighting stores, you're mostly limited to SPT-1 18AWG or SPT-2 16 AWG (used mostly in ordinary extension cords).