Thus, Joy, here is the best response I can muster.
anne of green gables
We can hardly start talking about flawed heroines without running headlong into this red-haired girl, who broke a slate over a boy's head for calling her 'carrots.' Anne Shirley is nothing if not flawed. Her imagination is her most memorable feature, and while it brings charm and life to those around her, it is most certainly a double-sided blade. She has a temper to match the color of her hair; which of us does not remember her flying in Mrs. Lynde's face and calling her a sour old gossip? She could talk both hind legs off the proverbial mule (who is always getting, in my opinion, the short end of the stick). Less prominent, but perhaps more basic, are her struggles with pride and her propensity to hold grudges for ridiculously long periods of time.
pride & prejudice
We brought up Mr. Darcy's flaws last time, so it would hardly be fair to leave Elizabeth Bennet from the picture this time. She primarily represents the second half of Jane Austen's memorable title, for she judges upon appearance and is adamant concerning her own hasty opinions. (This is a trait shared by another well-loved heroine, Margaret Hale of North & South - understandably, perhaps, since Mr. Darcy and Mr. Thornton also share significant flaws.) Elizabeth has a sharp tongue, as well, a fault many of us - myself included! - can easily relate to. These flaws, like Anne's, are some of the most fundamental aspects of her overall literary character.
the scarlet pimpernel
Another heroine this list could not do without. Lady Blakeney, wife of the foppish Sir Percy, appears at first blush to be even more flawed than either Elisabeth Bennet or Anne Shirley. Though a commoner during the Reign of Terror, she is quite as proud as any aristocrat. Her revenging herself upon a man who wronged her and her brother leads to the death of the man's entire family by the guillotine. And, of course, when we meet her she is estranged from her husband, scornful (albeit deservedly) of his ways, and something of a flirt. When pressed between a moral Scylla and Charybdis, Marguerite is also willing to sacrifice her conscience to save her brother's life. The tension of The Scarlet Pimpernel pretty much revolves around Marguerite's moral flaws.
the queen's thief
Again, Eugenides, the Thief of Megan Whalen Turner's The Queen's Thief series, meets his match in the character of the Queen of Attolia. The Queen has attained her position as most monarchs of her kingdom have in years past: through brutality. She is willing to kill - and more particularly, to murder - to attain the safety and prestige of Attolia. Rigidly just, but almost never merciful, she will extract her pound of flesh from anyone who crosses her. Indeed, the Queen has few good traits at all. Turner only manages to procure the reader's sympathy by revealing the moral struggle that still goes on inside the Queen, and by showing how other, better-loved characters feel about her.
Judy Abbott, the heroine of Jean Webster's Daddy-Long-Legs, is not such an obviously flawed character as the above-mentioned protagonists; but like any good character, the defects are there. In escaping the rigidity of the orphanage in which she was raised, Judy naturally exercises her newfound freedom and pursues her own way in all things. She is frequently obstinate, sometimes rude, and quite willing to flout the little authority that "Daddy-Long-Legs" attempts to employ. Quite feminist and strong-willed, she can actually be rather irritating.
the gammage cup
This character, Muggles, is even less clearly flawed. In general, she is quite the stand-up gal, quiet, patient, the sort of character who minds her own business and lets others mind theirs. However, this personality lends itself to other kinds of flaws. Muggles can be too meek, too submissive, and more willing to be walked on than to risk defending herself - aspects of her personality that only serve to make her more uniquely amazing as a heroine. There are no fireworks about Muggles, as there are with Elizabeth Bennet or Marguerite Blakeny. She is a simple, normal person with simple, normal flaws. She aptly illustrates the truth that a character need not have prominent flaws in order for the reader to see his or her growth; the struggles may be much smaller than a hot temper or murderous grudges. The flaw need only be real, and the author need only bring it to light.