Gonna repost this here:
Life, Destruction, Money. How would these three connect?
Here's my take on Team Swag/Flare/Flair's business.
The thing that I think would best connect all three is nature.
They are probably disguised as a huge business firm that earns money from all sorts of industries (probably fashion, technology, etc...), abusing all the natural resources for their own good disregarding the miserable effects it had on nature, such as deforestation, erosion, chemical contamination, pollution, and loss of biodiversity. Because of this, one of the legendaries would probably go on an outrage, while the other seeks your help to stop the evil team (but tests you first as always), as well as end the other legend's rampage.
This team might not be seeking out the legendary, much like how Rocket was. All they just care about is profit.