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Counterspell requires the following:
[a reaction], which you take when you see a creature within 60 feet of you casting a spell
The Flameskull's spellcasting block reads the following:
[The Flameskull] requires no somatic or material components to cast its spells.
If the Flameskull requires no visible components, can its spells be counterspelled?
Just because the spell has no visible components doesn't mean you can't see a creature casting it. Because the flameskull's spells still require verbal components, you know when it is casting a spell as long as you can hear it. If you see a creature and you know it is casting a spell, then you see it casting a spell, which satisfies the requirement for casting Counterspell.
If you were deafened, or if there was an area of silence or some other reason that you couldn't hear the verbal components of the flameskull's spellcasting, or if the flameskull casts a spell with no verbal component1, then you would be unable to perceive any components of the spell, and therefore you would not know the spell was being cast until after it took effect and it was too late to counter it.
1not possible without homebrew, since all the standard flameskull's spells have verbal component
