Choose one of your known Warlock cantrips that deals damage. You can add your Charisma modifier to that spell’s damage rolls.

Repeatable. You can gain this invocation more than once. Each time you do so, choose a different eligible cantrip.

The app doesn't allow it most likely because it would cause eldritch blast to glitch out, but, RAW, at level 2, can a warlock use two of their invocation slots to apply this invocation to, for example, Eldritch Blast and Booming Blade?

Yes? I believe that's what it means when it says you can do so.

I just wasn't sure if it was meant as "take it once at level two, and again at five."

That is definitely not what it means.

That's the intent, yes, and also for Repelling Blast. There's an example in this pre-release article:

Some Eldritch Invocations Can Be Repeated

Popular Eldritch Invocations for Warlocks like Agonizing Blast and Repelling Blast are still here but with a couple of big changes.

First, they are no longer limited to Eldritch Blast. Instead, you choose one of your known Warlock cantrips that deals damage, and now you can add your Charisma modifier to that damage roll. So now you can boost damage for Toll the Dead or Thunderclap with Agonizing Blast if that suits your Warlock build better than Eldritch Blast. Note, however, that Repelling Blast is restricted to cantrips that deal damage via an attack roll.

Next, you can select these invocations multiple times when adding new Eldritch Invocations. So if you’re trying to build a cantrip powerhouse, you could add Agonizing Blast or Repelling Blast to multiple cantrips. But of course, you still can use it for Eldritch Blast because, let’s face it, if you’re a Warlock, you’re probably going to want to.

Quote from MobiTraveler >>

 [...] The app doesn't allow it most likely because it would cause eldritch blast to glitch out, but, RAW, at level 2, can a warlock use two of their invocation slots to apply this invocation to, for example, Eldritch Blast and Booming Blade?

 I missed commenting on one thing regarding this part.

The interaction between Agonizing Blast and Booming Blade, Green-Flame Blade, or True Strike is under debate, but I'd like to leave my updated interpretation here, now including True Strike:

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The key to knowing if Agonizing Blast applies to one of your Warlock cantrips is checking whether the cantrip involves a spell's damage rolls, as stated in the Eldritch Invocation:

Agonizing Blast
Choose one of your known Warlock cantrips that deals damage. You can add your Charisma modifier to that spell’s damage rolls.

And the weapon attacks in Booming Blade, Green-Flame Blade, True Strike are not spell's damage rolls.

For Green-Flame Blade, starting at 5th level, you could technically apply Agonizing Blast to the Fire damage:

• "At 5th level, the melee attack deals an extra 1d8 fire damage to the target on a hit, and the fire damage to the second creature increases to 1d8 + your spellcasting ability modifier [...]"

For Booming Blade, the Eldritch Invocation could affect the damage rolls for Thunder damage:

• "[...] If the target willingly moves 5 feet or more before then, the target takes 1d8 thunder damage, and the spell ends."
• "At 5th level, the melee attack deals an extra 1d8 thunder damage to the target on a hit, and the damage the target takes for moving increases to 2d8 [...]"

And for True Strike, the Eldritch Invocation could affect the damage rolls for the extra Radiant damage:

• "[...] Whether you deal Radiant damage or the weapon’s normal damage type, the attack deals extra Radiant damage when you reach levels 5 (1d6), 11 (2d6), and 17 (3d6)."

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