She can sue him, but it is unlikely she would be successful in doing so. Without written contracts, oral agreements (under the statute of frauds) are enforced only when partial performance has been rendered. He made an oral agreement with her to clean the gutters, but it is vague since no time limit was set to perform. Also, his promise to pay (work of the deductible) would have to be in writing to be valid and thus, her chances of success if she sues would be limited, even more because she would have to prove it was the gutters that caused the flooding which she will have a hard time doing since the other house did not flood under the same conditions.
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