Magic Resistance:
The flameskull has advantage on saving throws against spells and other magical effects.
Turn Undead:
Each undead that can see or hear you within 30 feet of you must make a Wisdom saving throw.
Is Turn Undead magical?
Magic Resistance:
The flameskull has advantage on saving throws against spells and other magical effects.
Turn Undead:
Each undead that can see or hear you within 30 feet of you must make a Wisdom saving throw.
Is Turn Undead magical?
Channel Divinity is described on PHB pp 58 (emphasis mine) as:
At 2nd level, you gain the ability to channel divine energy directly from your deity, using that energy to fuel magical effects: Turn Undead...
This clearly marks Channel Divinity as a magical effect, and the Magic Resistance of the Flameskull would be triggered for advantage on the saving throw for Turn Undead.
As for the 2nd question, Magical Resistance is ONLY active against:
Spells and other magical effects
If something isn't a magical effect or a spell, then Magical Resistance isn't triggered. A more complete answer can be found on your other question.
PHB 58:
At 2nd level, you gain the ability to channel divine energy directly from your deity, using that energy to fuel magical effects.
Because Turn Undead is a channel divinity effect, that means that it's subject to magic resistance.
I didn't find a definition for "other magical effect," but I'd hazard that it's any effect that is magic but is not explicitly a spell. Magic Resistance doesn't protect against every saving throw; otherwise, it would work on purely mundane things like traps or the Battle Master's maneuvers.