Flameskulls have the following traits (Monster Manual, p. 135):

Eldritch Rejuvenation. A flameskull's shattered fragments reform unless they are splashed with holy water or subjected to a dispel magic or remove curse spell. If it can no longer fulfill its intended purpose, the re-formed flameskull is beholden to no one and becomes autonomous.

Rejuvenation. If the flameskull is destroyed, it regains all its hit points in 1 hour unless holy water is sprinkled on its remains or dispel magic or remove curse spell is cast on them.

If you defeat a creature like a flameskull, and wait for an hour until it rises again, then you kill it again, wait another hour, and kill it yet again... would you earn the XP each time you kill it? (Basically making an XP factory.)

Is there any rule which forbids that exploit?

Related question on turning defeated enemies into undead to defeat them again. This question differs from it because the creature is returning by its own natural ability and not a mechanic provided by an adventurer, which might affect whether it counts as “defeated” for the purpose of earning XP.

No

The DMG says:

Each monster has an XP value based on its challenge rating. When adventurers defeat one or more monsters — typically by killing, routing, or capturing them — they divide the total XP value of the monsters evenly among themselves.

Until the Flameskull has been defeated you get no XP for it. It is not (necessarily) defeated by being reduced to 0hp; this is an example of what defeat might look like that is not applicable for this particular monster.

If the objective of the PCs is to get past the obstacle the Flameskull represents (e.g. to loot the treasure it’s guarding) then it is defeated when they do that. If their objective is to destroy it, then it’s defeated when the sprinkle its remains with holy water. Whatever the objective is, it can only happen once and the DM decides when that happens.

Now, it’s perfectly reasonable to defeat an enemy more than once if circumstances warrant: for example, they could defeat the Flameskull by getting its treasure and then, after learning of its regeneration ability and how to stop it they could defeat it again with this new objective.

You can do this... kinda.

The Dungeon Master's Guide has this to say about awarding XP (page 260):

When adventurers defeat one or more monsters --- typically by killing, routing, or capturing them --- they divide the total XP value of the monsters evenly among themselves. [followed by clarification]

A literal reading suggests that you can kill the same enemy several times in order to gain its XP value many times. However, a more literal reading says that it's not the killing itself that counts --- it's defeating an enemy. The distinction is very meaningful when considering creatures that might not stay dead, such as flameskulls.

Consider a party in an enclosed space where they are constantly hounded by the same flameskulls, over and over again, until they find a way to destroy or evade them permanently. It would be a reasonable RAW judgment from the GM that killing the flameskulls does not constitute defeating them in this case --- you're merely inflicting a very temporary setback. However, in a dungeon where the players are expected to face an encounter of flameskulls and leave before their respawning can happen, killing them effectively accomplishes the players' objective and a reasonable RAW judgment would be to award the players the XP.

However, standing around a slain flameskull, waiting for it to reform, is not defeating it again. It's just toying with it --- there's no real or additional challenge involved in getting an easy kill from a just-reformed flameskull. As you can see from these examples, what exactly does defeating an enemy mean is somewhat ill-defined and therefore this scheme is dependent on the definition used by the GM.

Chances are no GM will let you farm XP

Experience farming is boring, and boredom shouldn't be a part of a TTRPG. Most GMs would either bluntly decide to no longer award experience for grinding, or come up with a creative punishment for trying to mess with the system. If you want a higher-level character, work it out with your GM instead of trying to subvert the rules.

RAW, yes - this is technically a workable exploit

Regarding Combat XP, the DMG simply states (emphasis mine):

Each monster has an XP value based on its challenge rating. When adventurers defeat one or more monsters — typically by killing, routing, or capturing them — they divide the total XP value of the monsters evenly among themselves.

Defeating doesn't necessarily mean killing

Technically, you are just defeating it, letting it reform, and then killing it again.

Whether or not the defeat is XP Worthy is up to your DM:

It's going to be up to the DM

While this is the technical rule, it is completely within the purview of your DM to say "stop this shenanigan...we're moving on."

And they can say this via RAW.

If the destroyed flameskull is not finished off, then it can be ruled that you haven't actually defeated it.

in order to truly defeat it, you've got to finish the job by sprinkling holy water or by casting dispel magic or remove curse.

This will all be up to the DM to determine when they think the creature has been defeated.

Yes, but...

It's not that big of a deal. As NautArch points out:

Regarding Combat XP, the DMG simply states:

Each monster has an XP value based on its challenge rating. When adventurers defeat one or more monsters — typically by killing, routing, or capturing them — they divide the total XP value of the monsters evenly among themselves.

Technically, you are just killing it, letting it reform, and then killing it again...but have you really killed it?

If your DM determines that this is a valid "XP factory" and that killing it is the same as defeating it, you're going to have to understand the cost of such a factory.

A Flameskull has a challenge rating of 4 and is worth 1,100 XP. Assuming you have a party of 4 players at level 4, each time you kill the Skull, each of you gains 275 XP. 275 XP per hour at the cost of fighting a creature that can cast a myriad of spells unlimited number of times is not that much. With the bare minimum of 2,700 XP required to be level 4, it would take you 14 hours and 14 encounters with this skull to get to level 5 and another 28 hours and 28 encounters to get to level 6.

Think of the cost of fighting a creature with 40 HP, 13 AC, with multiple resistances, immunities, and condition immunities. It's not as easy as killing it instantly, because if you can't kill it instantly, it can cast a fireball every time it resurrects. Or, it can flee, attack, or otherwise drag out the encounter to make itself more deadly.

Generally speaking, characters aren't meant to have 14 medium-challenge encounters a day and aren't equipped to fight that many times without long resting. It's not much of an exploit, it's more of a strategy with a big cost. And if you want to continue fighting it, you can't ever stop to long rest or leave it alone for more than an hour because, in all likely-hood, it will flee or otherwise do something to stop your strategy (or make it difficult).

This says nothing about whether or not your DM actually lets you do this in a vacuum or do it at all. But yeah, if you want to make a very slow XP grinder, you can do it.

Let's say you're working in a factory, assembling some kind of electric devices.
With the first one you struggle, and get some experience. The next one is faster; you don't learn that much by assembling it. By the end of the first week you won't get any more experience if you do the same thing again and again.

Similarly, you defeat a monster: it's challenging, you get experience. You defeat it again, it's somewhat less challenging, get some XP. By the time you defeat the 100th identical monster, you know their every single ability, you know how they try to dodge your attacks, everything.

I know an RPG system (somewhat based on AD&D) where this is explicitly stated. If in 5e it isn't (I'm not sure), that's a bug needs to be fixed. But the DM can override every rule, and - in this case - he should.