Most states in the United States have seals depicting a composite or symbolic scene. Many states then proceed to use these seals as the basis of their flags. A good example would be the state of Minnesota:

Manifest Destiny for the win! Wikipedia.

But you call that a flag?! Wikipedia.
Unfortunately, more than half of all the states in the Union have flags of this nature. I need hardly point out that this is poor flag design. A flag should not be ornate – it should be simple and recognizable. If it is, a useful side effect is that it can inspire any number of logos based on it, all of which instantly suggest the state in question. What happy states are these!

Wikipedia.

Nashville Predators NHL team shoulder patch. icethetics.co

Tennessee Titans NFL team. Wikipedia.
1. The Tennessee flag features three stars in a circle. This beautiful and simple device has inspired a number of logos.

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Baltimore Ravens NFL team logo. My Logo Pictures.

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2. The Maryland flag is very distinctive, featuring the quartered Calvert-Crossland arms, which appear all over the place in that state.

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easternscheritage.com

discoversouthcarolina.com
3. South Carolina is instantly recognizable by its palmetto and crescent, which appear in many things associated with the state.

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4. Then there’s the three pillars and an arch of the state of Georgia. People don’t make nearly as much use of this as they ought to.

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Arizona Coyotes NHL team secondary logo. Sportslogos.net.

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5. Arizona’s starburst is very distinctive and has inspired a number of logos.

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Dallas Cowboys NFL team logo. Wikipedia.

Houston Texans NFL team logo. Wikipedia.
6. Texas is the Lone Star state, which makes Texan logos all too easy.

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Columbus Blue Jackets NHL team logo. Wikipedia.
7. Another flag that deserves more use is that of Ohio, the only one in the Union that is not rectangular.

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Bear Flag Museum.
8. California’s bear and star make for a nice combination.

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9. Some folks like Rhode Island’s anchor, which is adaptable for all sorts of situations.

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10. New Mexico’s flag, featuring the red sun symbol of the Zia people, can be employed to a certain effect.

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11. Indiana’s torch and stars device enjoys a certain popularity.

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Colorado Rockies NHL team logo. Wikipedia.
12. Finally, there’s the stylized “C” of Colorado’s flag. This design dates from 1911 and seems quite ahead of its time.
Of course, many states still have recognizable logos or images, even though their flags aren’t that well designed. Wyoming and Pennsylvania (the Keystone State) come to mind:

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“Bucking Horse and Rider,” a registered trademark of the state of Wyoming. Wikipedia.

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And as the logos reproduced above for Indiana and Arizona show, a state’s outline provides a ready-made image for the state in question. Americans love these jigsaw-puzzle pieces. I think what makes American state outlines so memorable is the combination of straight with squiggly lines. Whereas it would take effort to distinguish between the shapes of (say) Staffordshire and Wiltshire, apart from Hawaii all US states have at least one straight border, “anchoring” their shapes so to speak in one’s memory (although the shapes of Colorado and Wyoming, both square quadrilaterals, suffer the opposite problem).
But the fact remains that the overall standard for US state flags is rather low.

University of Wyoming Athletics logo. Wikipedia.
UPDATE: You could read Wyoming’s bucking horse rider as either male or female, but the rendition above looks male to me, and I would be not be against inventing a variant that presents as female, perhaps through the addition of a ponytail. I’m surprised that the University of Wyoming, whose teams are the “Cowboys” and “Cowgirls,” does not do this already. Governmental usage could then alternate between the two renditions, which would be especially appropriate for the Equality State.