Allays that have an item can be damaged by the player who gave them the item with a fire aspect sword. This does not apply to the flame enchantment on bows. When hit, the allay will start burning as is the case with other mobs, but allays are meant to not be able to be hit by their owners.
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We're tracking this issue in MCPE-156785, so this ticket is being resolved and linked as a duplicate.
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