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If I attack one part of an uncombined Sky Shadow, and a triggered ability KO's that part before flipping cards resulting in Sky Shadow combining, does the attack end? Or does the attack continue against the combined Sky Shadow?

The attack continues since "Combiner Mode" is mostly another mode like Alt or Bot mode. You just can't "flip" to combiner mode without another card telling you to. Going to combiner mode is a one-way operation. Note that Sky Shadow will be untapped because the process of combining creates an untapped character.
Source: Wizards of the Coast (2020-06-10)    【Link to Ruling】
Tags: Sky Shadow (Plane), Sky Shadow (Tank), Sky Shadow, Elite Warrior, Sky Shadow Sync