I believe that when a system requires a permit, you need to build up reputation with the faction that controls the system in order to get a permit.
Look at the galaxy map to see what faction controls the system, find systems (or at least stations) they control that you can get to, look in the bulletin boards, and run some missions for them.
Update:
I believe this answer is correct for that system, however, for a number of Federation and Empire controlled systems, you need to build up rank instead of reputation with those major factions. You get rank by doing missions for Federation/Empire affiliated factions until you get a Federation/Empire Naval mission and then doing those missions.
Federation systems requiring Federal Navy rank: Sol, Beta Hydri, PLX 695, Ross 128, Exbeur, Vega, Hors (list probably not complete)
Empire system requiring Empire Navy rank: Achenar, Summerland, Facece (list probably not complete).
Note: in my experience, you get the permit in the form of a "go to system X to pick up another mission, and here's the permit" type mission, and if you go to that system, there's nothing special...
Also, there are some systems that are just plain locked down, with no way to get a permit. I believe these are there for some possible future additions to the game. I don't think any of those show up as having stations in them, though.
Check your Contacts tab on the left panel of your ship. If they show up as wanted, it'll show the amount in their entry in the Contacts tab.
It's worth mentioning that this won't show all of their bounties until you scan them with a Kill Warrant Scanner, so if they have bounties from other systems as well, you won't be eligible for those without the scan.
Best Answer
I believe that "these goods are unique to this mission" means you're looking for a mission-specific signal source, not just any signal source holding trade data.
Sometimes scanning the nav beacon (drop in and get a scan of the actual beacon) can help (leads to a mission update message giving you a more specific location).
Scan all the signal sources until you find a mission-specific one. It will be really obvious after you scan it (different color, clearly says it's for your mission, etc).
It's also possible that you found a bugged mission. Sometimes that happens, and there's no way to actually complete it.
I'm not sure I've actually done a "trade data" mission, but I have definitely done some "exploration data" missions, so the mechanics should be similar.