Most of the air is removed from the gap between a vacuum flask’s inner vessel and outer shell. With too few gas molecules to carry energy, conduction through the air is greatly reduced. The absence of circulating air also almost eliminates convection. This is the vacuum layer’s main job.
A vacuum, however, does not mean that heat cannot cross the gap. The warm inner vessel still emits infrared radiation, which does not require air; energy from the Sun likewise crosses the vacuum of space. Flasks often use reflective surfaces to reduce this transfer, but they cannot remove it completely.
Some parts cannot be separated by vacuum. The inner vessel must connect to the outer body around the neck, while the stopper, seals and supports are solids through which heat can conduct. Opening the lid also allows warm air and water vapour to escape directly. A fuller flask that is opened less often will therefore usually cool more slowly.
A vacuum flask does not create a place where temperature never falls. It reduces three routes of heat transfer—conduction, convection and radiation. This delays the approach to room temperature without overturning the tendency of heat to flow from warmer regions to cooler ones.
https://bsesc.energy.gov/energy-basics/heat-flow
https://www1.eere.energy.gov/education/pdfs/basics_thermodynamicsguideteacher.pdf
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