When you add insulation, your body heat is first used to warm it up. The amount of heat to warm up an OverShell jacket very much depends on the density of its insulation - related to its thermal mass. Heavy linings take more energy to warm up before the insulation becomes effective.
Blizzard kit is very light so has a low thermal inertia (and reflects heat radiation).
By wrapping an OverShell jacket in your flask you have a jacket that is already pre-warmed, reducing the thermal inertia effect.