I don't see how the existence of insulanium violates any of the laws of thermodynamics :
The 1st Law is a statement that energy is conserved. But there is no suggestion that energy is being created or destroyed here.
The 2nd Law states that the entropy of an isolated system only increases, never decreases. This is not saying that the entropy cannot stay the same for a very long time. When "forever" is reached, the insulanium will be at the same temperature as the contents of the flask - and/or its surroundings. The entropy will then have increased. The fact that it takes "forever" to reach thermal equilibrium is not a violation. Neither is it being claimed that the insulanium will get colder while the contents get hotter. That would violate the 2nd Law.
The 3rd Law states that any isothermal reversible process always increases entropy, except at absolute zero when $\Delta S=0$. No reversible process is being performed here. So I don't see how this Law applies.
The only thing I can find "wrong" with the description of insulanium is that its properties are not well defined. How long is "forever"? In physics - well, in engineering and technology! - unlike maths, we do not deal with infinities, and we have to be careful about zeros also. "Forever" could mean 10 years, which is far longer than any domestic thermos flask could keep something warm. It could mean 1000 years. That would be incredible, but it is not physically impossible.
Likewise, the tolerance for 100% reflectivity is undefined. Is this >95% or >99.5% or >99.995% or what? Even within a stated tolerance, "perfect" reflectivity at all wavelengths might be unrealistic but it is not physically impossible. We define a blackbody as an ideal absorber/emitter at all wavelengths. Although no real material with this property exists, it would not violate the laws of physics if it did.
Insulanium might have unrealistic properties. It might be highly unlikely that it could ever exist. But as far as I can see it does not violate any laws of physics.