Here's why:
* Different Game Engines: Sonic Advance and Sonic Adventure 2 Battle are completely different games with distinct game engines and save data formats. They are not designed to be compatible with each other.
* No Built-in Transfer Feature: There is no built-in feature or mechanism within the games that allows transferring Chaos or any other data between them.
While there are some ways to transfer data between different versions of the same game (like transferring save files between Sonic Adventure DX and Sonic Adventure 2 Battle), there is no method to transfer Chaos or any other data between Sonic Advance and Sonic Adventure 2 Battle.
If you're looking to raise Chaos in Sonic Adventure 2 Battle, you'll need to start from scratch and nurture them within the game's Garden.