Black Market definition in terms of Kingdom Building
If you look through later, you'll see that larger areas may also contain a Black Market (like the Waterfront), which allows you to buy illegal items.
When you use Diplomacy to Gather Information about the Black Market, if you make a successful check, you treat it as part of a Settlement that's 3 sizes larger than the Settlement actually is, for the purposes of determining the available (illegal) items, and also gain the ability to sell stolen goods therein.
So, if you make a Gather Information check in a Small Town, the Black Market there will count as one in a Large City instead, and you can sell stolen goods as well as buy. If the Settlement you're currently in is bigger than a Large Town (which would be upgraded to having a Black Market equal to that of a Metropolis), the Talent explains what items are available, although you are still allowed to sell regardless.
The DCs to make a successful GI check are listed as part of the talent
So, reading it, it seems that once you make a successful GI Check, you can buy and sell to your heart's content (you don't need to make a check EVERY time you buy or sell).
Whether that is PERMANENT, or whether that resets once you LEAVE the Black Market is really up to your GM - you could establish permanent connections in the Market with just that Diplomacy Check, or you may need to make a new Check every time you enter because of the ever-changing nature of dealing with organized crime.