The Channel Divinity element of the Paladin's Sacred Oath class feature (Player's Handbook p.85) says:
Some Channel Divinity effects require saving throws. When you use such an effect from this class, the DC equals your paladin spell save DC.
The Paladin Spellcasting class feature specifies what that DC is:
...you use your Charisma modifier when setting the saving throw DC for a paladin spell you cast and when making an attack roll with one.
Spell save DC = 8 + your proficiency bonus + your Charisma modifier
In general, if your class has a Spellcasting class feature, the spell attack and save DC listed there will be the right ones to use for any magical class features. It's certainly possible there are examples where that isn't the right choice, but it's a good first guess if you aren't sure.