Well, after crafting a campaign just recently, and having a great villain, I have come to a sort of writer's block. I have no idea what my villain should be, and am completely stumped. 

If you're wondering what the campaign will be about, it is as follows: 

At the start of time, there were seven demons, and seven angels. Between them was everlasting war. And it seemed like the war would go on forever. But, the angels had a secret weapon. They crafted seven flames, which could act as prisons for the demons. Really long story short, the angels trapped the demons inside the flames, and the angels created civilization. But recently, something has been going wrong. The flames have been flickering and getting smaller. Someone has been doing this, and for some reason, they want to release the demons. 

Any ideas fellow DMs?

Depends. How does this universe work with the Nine Hells and the Abyss? Is Asmodeus around?

And now I want to make a story where the characters are (knowingly or otherwise) working for Asmodeus to prevent the release of demons that were imprisoned by celestials with the celestials having stopped worrying about them because the seals were permanent unless someone went and broke them out.

For the OP, could be the demons adapted to the seals enough to promise someone power in exchange for doing certain acts, now whether they will get the power or just get killed by demons is entirely up to you. 

Alternately, one of the demons planned ahead and planted a seed of some sort that would eventually release them.

Yes and yes. All demons in the forgotten realms are around,  but the demons in the flames are not regular demons. But rather spirits or primordial destruction. (Ex: Fear, Pestilence) Imagine the horsemen of the apocalypse but, seven of them. The Nine Hells and Abyss are around, but these are different demons.

So, a possible villain idea: 

A Dwarf Jester named Xorthrison, who has been fired from the King's Court due to being, "An unfunny little pipsqueak" And it just so happens (Go figure) that Xorthrison has chosen to walk by one of the places that a Shadowflame is being held. This place would happen to be an unmarked tomb that has been unopenable for centuries. Something calls Xorthrison from inside the tomb, and he walks into it, opening the door easily. The Flame near him flickers, and him being so close to it, leaps down his throat. 

Or something along those lines perhaps.

Use something like The Mule from the Foundation Series, the Angles have not been able to predict someone like that who is able to create chaos 

A cult of elemental worshipers are tapping into elemental energy.  This is causing the change in the ability of the flames to work as needed.  The cult is the first tier of the problem, but there are a band of clerics forming the cults around the area.  And these clerics are being led by an evil Triumvirate of Warlocks that understand the true nature of the object to free the demons.  The party has three levels of challenge that will need different skills to address.  The average cult worshipers will need to be dealt with by clerics, rangers and druids that can root them out and teach them the error of their ways.  The Clerics will need to be dealt with by forces that can counter their spells such as Clerics and Paladins.  And the warlocks will need to be dealt with by high level PCs ready to deal with anything.

Just had a fun idea, cult of celestial worshippers finds seven sources of seemingly endless radiant energy and starts using them to do good, not realizing they're drawing power from the seals on the seven demons.  The PCs may be able to convince them to stop, but likely not before at least a couple of the demons get out and start trying to release the others.

Oh, that could be fun. I'll keep it in mind.