Shame on me!
I had never heard of any indigenous Native American usage before. But because of this thread I decided to investigate a little more.
http://www.straightdope.com/columns/read/440/was-the-swastika-actually-an-old-native-american-symbol The Nazi fylfot, known as the swastika or hakenkreuz ("hook-cross") is actually a Teutonic runic ideograph called "Thorshamarr"--"the hammer of Thor." Although the Nazis emphasized the aggressive, martial implications of this symbol, its primary traditional meaning was the solar wheel and the cycle of life. The Thorshammarr, like many other runes and ideographs, was depicted in reverse (mirror-image) frequently, but its meaning remained constant. The concept of deosil (clockwise)/widdershins (counterclockwise) opposition, which occurs in European magical practice, does not apply to Teutonic runes.
The fylfot occurs frequently in native American symbology, and may be found in Northern Plains beadwork and Southwest pottery, basketry and sand paintings--usually with a deosil orientation. In Northern Plains symbolism, the fylfot is a representation of the four directions, and embodies the concept that the sacred place of two-leggeds (humankind) is at the center of the world-hoop. Even today the circular solar wheel is reproduced in hair ornaments of rawhide wrapped with dyed porcupine quills, traditional pieces which are still being made by Lakota craftswomen in the manner of their ancestors. --Jean-Marie E., Goleta, California
And then I even found buried in the original Wiki a section on Native American swastikas:
The swastika shape was used by some Native Americans. It has been found in excavations of Mississippian-era sites in the Ohio valley. It was widely used by many southwestern tribes, most notably the Navajo. Among various tribes, the swastika carried different meanings. To the Hopi it represented the wandering Hopi clan; to the Navajo it was one symbol for a whirling winds (tsil no'oli'), a sacred image representing a legend that was used in healing rituals (after learning of the Nazi association, the Navajo discontinued use of the symbol).<37> A brightly colored First Nations saddle featuring swastika designs is on display at the Royal Saskatchewan Museum in Canada.<38>
A swastika shape is a symbol in the culture of the Kuna people of Kuna Yala, Panama. In Kuna tradition, it symbolizes the octopus that created the world; its tentacles, pointing to the four cardinal points.<39>
In February, 1925, the Kuna revolted against Panamanian suppression of their culture, and were granted autonomy in 1930; the flag they adopted at that time is based on the swastika shape, and remains the official flag of Kuna Yala. A number of variations on the flag have been used over the years: red top and bottom bands instead of orange were previously used, and in 1942 a ring (representing the traditional Kuna nose-ring) was added to the center of the flag to distance it from the symbol of the Nazi party.<40>
Native American basketball team in 1909.