American English doesn't have quite the divergent dialect issue that British English has, but it most certianly does have its own dialects.
What you generally hear from folks on TV is what is called Standard American English. "Don't got" would indeed be fairly unusual in that dialect, and would fall oddly on a SAE listener's ears.
However, there are other dialects where that is quite common, most notably African American Vernacular English, along with those spoken by many poor rural white folks. Features of AAVE are often found on USA TV shows (even coming from non-African Americans) to indicate that the speaker comes from a rough urban environment.
Here's what wikipedia says about AAVE and negation:
Negatives are formed differently from standard American English:
- Use of ain't as a general negative indicator. As in other dialects, it can be used where Standard English would use am not, isn't, aren't, haven't and hasn't. However, in marked contrast to other varieties of English in the U.S., some speakers of AAVE also use ain't instead of don't, doesn't, or didn't (e.g., I ain't know that). Ain't had its origins in common English, but became increasingly stigmatized since the 19th century. See also amn't.
- Negative concord, popularly called "double negation", as in I didn't go nowhere; if the sentence is negative, all negatable forms are negated. This contrasts with Standard English, where a double negative is considered incorrect to mean anything other than a positive (although this wasn't always so; see double negative). There is also "triple" or "multiple negation", as in the phrase I don't know nothing about no one no more (in Standard English "I don't know anything about anyone anymore").
- In a negative construction, an indefinite pronoun such as nobody or nothing can be inverted with the negative verb particle for emphasis (e.g. Don't nobody know the answer, Ain't nothin' goin' on.)
Given the skewed demographics of the US prison population, I think you could expect to hear AAVE or some poor rural dialect spoken in a prison scene, and would not expect to hear SAE.