So I had an idea for a campaign I'm running- an evil-aligned party who essentially slowly turn into BBEGs. Has anybody done something like this before, and if you have, any tips?

The primary reason why Good tends to triumph in the end is that Evil tends to turn against itself.  Look into the "Bloodwar" if you want to know about the way Evil behaves.  Your idea should be a lot of fun if you enjoy interparty conflict, with lots of backstabbing (sometimes, between the characters with a dagger) and political maneuvering.

I have never tried to do this.  In my own experience, I've never seen it turn out well.  Asking players to be Evil, if they play anything resembling the way Evil is typically presented, leads to arguments in the real word, and getting people's feelings hurt.  Lawful ones are going to quibble about status and who gets to be the boss, Neutral ones are uncaring and only in it for themselves, and Chaotic ones actively seek to encourage everyone to do more harm. 

I did run several evil groups in the past and they usually end up as murder hobos killing everything they come accross or end up turning against each other. I rarely saw it end well, it really takes people that understand and play within all the subtilities of evil alignment spectrum and not just stick to the serial killer syndrome or things end up ugly or sour eventually.

Based on the other pieces of advice I would suggest giving each player an agenda that really really needs to other players to make it work. All their plans would fail if the other PCs refused to help them. That would put everyone on their best behavior towards each other. Another solution would be to have a good party as their rival. Not actual PCs, just an idea of something more powerful then them that they must grow to defeat.

For the having the players be BBEGs- that might be difficult. Player characters are glass cannons whereas monsters typically have more HP and less damage output. Scaling for PCs vs PCs isn’t really a thing.

We sort of did this. The DM ran a campaign set in Tal'Dorei (Critical Role).

We had a main party of good aligned characters and a side party of evil characters (working for the hobgoblin empire).

The evil party was doing evil things like stealing doomsday weapons and slaughtering halfling villages. In the end it turns out they were double crossed and the end of the campaign was both parties (so each of us playing 2 characters) working together to stop the campaign BBEG.

Of course when the evil party returned home they promptly took control of the empire and are biding their time to strike and take over the rest of the continent.

The best evil campaign I have ever been a part of was run very much like a paranoia game, very tongue in cheek every player had an agenda that was diametrically opposed to at least one other players, so lots of backstabbing. The characters understood as a small group in a large generally good nation they needed to keep below the radar so murder hoboishness was limited. But all the players and the DM where experienced and the game was designed to just last 10 sessions. 

I wish I was still playing in our evil campaign; it was so much fun. The thing you have to understand (that's been touched on by just about everyone now) is that PVP will be common in a evil game. you just kinda have to accept that and roll with it. I think it made the games hella fun.

I guess it depends on what you think the players would want to do?

If they want to just kill everything or backstab each other, then the group needs to be okay with that. Characters backstabbing each other could cause a lot of friction...

Personally, I think being the bad guy could be really cool and an evil campaign could work well. My idea of what would be fun though is the scheming and plotting and trying to create my evil empire. There are a lot of cool role play elements to building out your evil network and recruiting minions and setting the stage for your evil plot to take form and then be revealed! The other player characters would be part of our evil consortium where we need what each other brings to the table to bring out grand plans to fruition. This helps reduce interparty potential feuds or backstabbing, at least for some of the time. Perhaps the last battle is against each other for the rights to rule it all!

Just don't take it too seriously. Evil campaigns will by their nature fall apart spectacularly, sooner or later. So have some crazy fun, let the group implode, cathartically mop up the survivors with some good guys, and move on. It's fun as long as you don't expect much!

I love the idea of them effectively competing to become the BBEG, but in a "working together" kind of way. 

I would love to run something like this, not least because I would weave the after-effects of their missions into the story of my next standard campaign with the same players, so they realise they are going to have to fight their previous character that became the BBEG.

Now, potentially you could have them agree to form an alliance to conquer the world. They can become BBEG's in their own right, but without the need for them to compete. Have them regarded as the losers of the evil world, and then have the other evil empires that they are fighting to gain control of start seeing them as an annoyance, then a problem, then a threat, as they grow in power. They throw assassins and honeyed deals and all sorts of things at them to try and cling to their evil kingdoms, and one by one are toppled and the kingdom taken over by a PC. This deposing of previous evils might push them into the path of future heroes. 

I can't stop hearing Oingo Boingo singing "Dead Man's Party" every time I see the title of this thread.

A good thing to set up front ahead of time is what kind of "evil" the group expects and is comfortable with. It's one thing to come into the campaign as Skeletor (evil yet still on the campy side of things) vs Hannibal Lecter.

You should ask how acceptable is PvP. And if a campaign where the PCs aren't fighting against each other, what incentive is provided for them to not betray and turn on each other at the earliest opportunity.

Ask to what degree of acceptableness is there for heavier and triggering subjects: sexual assault, torture, killing of children, and other topics. Even if included in the campaign, there's a range of differences from lingering details to off-screen fade to black.

Also ask how 'realistic' are your evil characters. A lot of fictional media has villains who know that they are evil, love it, and act one-dimensionally and genuinely do want a world where everyone suffers, including themselves. In real life there are some people like this, but overall are very rare. A lot of people who engage in wicked actions can still be cruel and sadistic, but often go through mental gymnastics to justify themselves, or start out as decent people but being in a cruel environment gradually wears down their levels of empathy. And some evil people aren't particularly sadistic or vindictive, they're just selfish. They just don't care if someone's getting hurt from their actions.

There's no real right answer to any of the above, but people coming into an evil campaign can have some very different sets of expectations. It's good to ensure that everyone's on the same page for these kind of campaigns.