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It's more about the usage. When you say in Russian "I gave flowers" it sounds unspecific, because, ultimately, you made your girl a present with those flowers. So she's the end user. But when you...

Also, as a side note, if you plan to use that phrase in a real conversation, I would suggest to rephrase it a bit:

Я дал цветы моей девочке
=> Я подарил цветы своей девушке