Farm City: The Education of an Urban Gardener, by Novella Carpenter. A close second would be Animal, Vegetable, Miracle, by Barbara Kingsolver. Both are non-fiction, written by real people doing real gardening. They are both far more ambitious that you sound, but the Kingsolver book might prove especially inspirational to you as part of the reason she writes it is to inspire people t garden. However, these memoirs are really about vegetable gardens. I'm a librarian who loves to garden both flowers and veggies, but I can't think of a single memoir about flower gardening.
On edit: you got me thinking about flower gardening memoirs. Found one I'm going to read now, maybe it will interest you, too. It is:
Slug tossing and other adventures of a reluctant gardener, by Meg DesCamp. Sounds really funny and maybe even inspirational. 
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