I heard it expressed on gotel radio station; "Don't go nowhere" can it be correct?
This is an example of a double negative. Traditional formal English considers these to be poor style. However these forms are fairly common in casual speech.
In the example the meaning is clear "Don't go nowhere." is equivalent to "Don't go anywhere". Sometimes the double negative introduces an ambiguity: "I don't know nothing about it" could be understood to be a casual way of saying "I don't know anything about it." or a way of saying "I do know something about it." (We will use a range of cues, such as accent, presumed age, class, context and expected meaning to understand which is meant.)
Learners should generally avoid these double negative forms, as they are generally considered to be "poor English". But be aware that native speakers will use them from time to time.