The paladin class states that
at 2nd level, when you hit a creature with a melee weapon attack, you can expend one paladin spell slot to deal radiant damage to the target.
The Death Cleric Domain states that at 2nd level
when the cleric hits a creature with a melee attack, the cleric can use channel divinity to deal extra necrotic damage
Can a death cleric/ paladin multiclass expend spell slots to deal extra damage with smite and stack channel divinity to deal extra damage on the same attack?
Certainly.
There are a number of ways to boost damage (or other stats). In general, if abilities don't have the same name, then they stack. Since they don't share a name, they stack. You can also add on other abilities. So, if your Cleric/Paladin picked up some levels in Rogue, you could get a Divinely Channeled Smite Sneak Attack with no problems.
If you're concerned this might be over powered, it's not. The reason is that Smite and Channel Divinity are limited resources; you can only do that combo once or twice per battle.
