> paint onto the outside of a vacuum flask, and have it be sucked into any gaps and solidify there.
Stuff like paint will tend to be very permeable- if it relies on a solvent drying out, then obviously its permeable enough to let the solvent through. Even if it does dry to a very solid state, there will be a very very long tail of evaporation of volatiles inside the substance.
> It seems they already make a product for that - vacuum grease.
Vacuum grease isn't perfect- it's not recommended for the high end of high vacuum or for UHV. Or for single digits of kelvin.
Another big factor is that if you're doing science, you probably want to go out of your way to eliminate contamination like that. Guessing about the possible chemical interactions of a secret proprietary substance under extremely low temperature and pressure is not a fun way to get your doctorate.