A vampire has charmed my fighter buddy and I wish to use my Hurl Through Hell ability to make the vampire briefly go to the lower planes, resulting in the charm being broken.

...when you hit a creature with an attack, you can use this feature to instantly transport the target through the lower planes. The creature disappears and hurtles through a nightmare landscape. At the end of your next turn, the target returns to the space it previously occupied, or the nearest unoccupied space.

However, I am not sure if the “hell” part is supposed to be merely fluff with no actual planar travel happening.

So does Hurl Through Hell cancel a vampire's charm effect?

Yes; Hurl Through Hell will remove the Charm Effect

The description of the Hurl Through Hell ability starts with the following description:

Starting at 14th level, when you hit a creature with an attack, you can use this feature to instantly transport the target through the lower planes. The creature disappears and hurtles through a nightmare landscape.

The feature says it "transports the creature through the lower planes", the "lower planes" in this context definitely being various alternate planes of existence. The Player's Handbook is direct about what the Lower Planes are, in its description of the various planes of existence, starting on page 301:

Beyond the Material

Beyond the Material Plane, the various planes of existence are realms of myth and mystery. They're not simply other worlds, but different qualities of being, formed and governed by spiritual and elemental principles abstracted from the ordinary world.

[...]

Outer Planes

If the Inner Planes are the raw matter and energy that makes up the multiverse, the Outer Planes are the direction, thought and purpose for such construction.

[...]

The planes with some element of good in their nature are called the Upper Planes. Celestial creatures such as angels and pegasi dwell in the Upper Planes. Planes with some element of evil are the Lower Planes. Fiends such as demons, devils, and yugoloths dwell in the Lower Planes.

So in this case, being "transported through the lower planes" is not merely fluff: by any literal interpretation of this feature (spells and features generally should be interpreted literally) the target creature must, between the attack that took place, and the end of your next turn, exist in the lower planes, and thus be on another plane of reality.

So if you're looking for a way to instantly end the Charm effect on your fighter friend, and don't have a ready-made way to end Charm effects, you'll be able to attack your Fighter friend the Vampire^*, invoke this ability, deal 10d10 damage (55 damage) to them, and end the Charm effect once the fighter and Vampire are in separate planes of existence.

^{* Of course, because no Warlock would ever attack their own friend, right? ;)}

Yes, this works fine

There is no such thing as 'fluff' in spell descriptions. Spells in 5e do exactly what they say they do.

Hurl through Hell

...when you hit a creature with an attack, you can
use this feature to instantly transport the target through the lower
planes. The creature disappears and hurtles through a nightmare
landscape...

And the Vampire's Charm power says:

Charm
...Otherwise, the effect lasts 24 hours or until the vampire is destroyed, is on a different plane of existence than the target, or
takes a bonus action to end the effect.

So yes, the Hurl through Hell ability does remove a vampire's Charm effect from its victims.