If you interact with the NPC on the top floor, you'll have the option to use the gun store and market. You do not need a firearms license to buy guns at the gun store.
If you complete the 20 second capturing process, you'll gain access to a weapons shop and market similar (but highly limited) to the one at a rebel outpost. The capture point is the small billboard next to the front door of the large Black Market building. When a gang captures a Black Market, a global notification will be send to everyone on the entire server.
Additionally, if you capture the Black Market, you'll be able to process drugs there. The Black Market takes 5% of the drugs you process at the Black Market. You will not be able to "double-process" drugs at the black markets.