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In Kingdom Hearts: Chain of Memories, the ability system is replaced by the Sleight and Enemy Card system. Sleights serve as the game's action abilities, are activated by playing card combos, and are earned by levelling up/getting a new magic card. The Enemy Cards serve the game's support abilities, and must be played to activate temporary status changes. They are earned by defeating a boss.
As for the Growth Abilities, Sora and Riku can use Dodge Roll as a default growth ability, by double tapping either directional button. In the remake, Sora later obtains the High Jump, Glide, and Superglide growth ability as the story progresses.