This is how Thunderwing and Queen Chrysalis team up goes in The Revenge of Thunderwing.
Queen Chrysalis: I am Queen Chrysalis, leader of the Changelings.
Thunderwing: I am Thunderwing, servant of Unicron the Destroyer.
Queen Chrysalis: I have come to....
Thunerwing: I know why you're here. You want revenge against Twilight Sparkle. Tsk tsk, your majesty. Playing around with revenge is a very dangerous thing.
Queen Chrysalis: I could have succeeded in conquering Canterlot had that pathetic unicorn not found me out! Perfect little Twilight. I want to make her pay for thinking she could humiliate me. But I can't act against her on my own. That is why I have come seeking your help.
Thunderwing: So what's the gig?
Queen Chrysalis: If you help me, I will help you to destroy the Matrix and Element of Magic.
Thunderwing: I'm listening.
Queen Chrysalis: We must get rid of them.
Thunderwing: Tell me, your majesty, what happens when you remove one of the Elements of Harmony?
Queen Chrysalis: I don't understand.
Thunderwing: Twilight Sparkle is the key to activating the Elements of Harmony's power.
Queen Chrysalis: Go on.
[Thunderwing shows Queen Chrysalis what he did to render the Elements of Harmony useless]
Thunderwing: Get Twilight to turn against her friends, show her the flashback where no one believed her when it was you disguised as Cadance. Make Twilight's friends the villains and only then will you be able to separate the others from her.
Queen Chrysalis: But how can I do that? She trusts them too much.
Thunderwing: Oh. It will be easy. With this! [holds up the Dark Spark]
Queen Chrysalis: What is that?
Thunderwing: This is the Dark Spark: the antithesis to the Matrix of Leadership.
Queen Chrysalis: What does it do?
Thunderwing: It does what the Matrix does only different. And it also corrupts an Equine's heart with my master's evil.
Queen Chrysalis: Neat.
Thunderwing: Glad you think so.
[Queen Chrysalis and Thunderwing laugh evilly]