You can't uninstall, you can't reset your profile and as long as your pin is valid on the Nike server it will continue to log your workouts to some diconnected account on their end. To fix this, you have to get your iPhone to invalidate your account.
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Install the trial version of Charles http://www.charlesproxy.com/download/
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Download the Charles certs and install them on your iPhone http://www.charlesproxy.com/ssl.zip
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Create a local map in Charles from
https://nikeplus.nike.com/nikeplus/v1/services/device/get_pin_status.jsp
to a local file with the following content.