Build bunkers and protected areas out of it.
In a comment, I cited an answer I wrote on Skeptics about Starlite and how it is, for all intents and purposes, a hoax. However, in that answer, I cited an article from The Telegraph that was pointed out by Bobson. According to the article, Starlite - well, some form of it, because little-to-no reputable information is available about any of the tests - survive a simulated nuclear explosion:
In June 1991, a sample was sent to White Sands atomic weapons testing site in New Mexico, in the care of the SAS, and subjected to a simulated nuclear onslaught. 'It was classed as the biggest bang in town. I've seen a video [on which] it shredded forest to sawdust, rolled some tanks around, stripped an aircraft into pieces.' But Starlite survived. Further tests at Foulness had subjected it to the force of 75 Hiroshimas, and it survived that, too.
What could one use a material that can survive a nuclear attack for? Well, if a solid chunk of Starlite - in other words, some three-dimensional shape - could survive a nuclear attack, then it could be used to protect some weapon or other important object during a nuclear attack that would be used in the aftermath.
Attackers could drop a weapon encased in Starlite during the drop of a nuclear bomb. Post-detonation, the weapon could itself be detonated, devastating the area again. Alternatively - and this is where the big advantage lies - it could be used in defense. If a military base was bombed, weapons could be encased in (or perhaps made out of) Starlite and used after the attack against any forces that came by. Soldiers and other important equipment would also be protected.
The best offense is a good defense, and if you can use Starlite to keep your weapons, personnel and military equipment safe, then you've got a pretty darn good offense.