If you flicker a creature with a triggered ability on the stack, does the trigger still resolve?

When a triggered ability goes on the stack, it becomes an independent object — separate from the permanent that generated it. Exiling and returning ('flickering') the source creature does not remove the ability from the stack. Per CR 112.7a, once an ability is on the stack it exists independently of its source.

The creature that returns is treated as an entirely new object with no memory of its previous existence (CR 400.7). So the trigger still resolves, but results may differ depending on how the ability is worded. If the ability targeted the creature itself ('this creature gets +2/+2 until end of turn'), the target is now a new object that was never legally targeted — the target is illegal and the ability is countered on resolution per CR 608.2b.

If the ability doesn't target the original creature, or targets something else entirely, it resolves completely normally. The flicker has no bearing on those effects.

Concrete example: Your Mulldrifter's 'When Mulldrifter enters the battlefield, draw two cards' trigger is on the stack. An opponent flickers Mulldrifter with Ephemerate. The draw-two trigger still resolves and you draw two cards, because it doesn't target Mulldrifter at all. Meanwhile, the new Mulldrifter that entered will generate a brand-new 'draw two cards' trigger of its own.

Summary: flickering the source never removes the trigger from the stack (CR 112.7a), but whether the effect fully works depends on targeting and whether the ability references the now-replaced permanent.