I have noticed that the way we answer the questions when we first become a Pirate affects the type, number and actual Companions that we get. If you want a particular Companion, check the Crown store frequently (they appear when badges are used) and they appear only when they would normally in the story line. So, if you haven't reached the point in the story line where they would normally appear, they probably won't be in the Crown Ship yet.
I'm sorry but all of these don't work I even finished the Rat Pack line quest (Well, because I like 100% these days). I checked The Frogfather every time but still no quest (Well, the only quest I got was a Cool Ranch main quest for Silver Bullets).
In order to get Tricky Vinny you must first do a quest for Strong John Silver, who is located in Gullet. After doing this quest John will tell you to go speak with the Frogfather, which is where you will be given Tricky Vinny if you are a swashbuckler.
Strong John Silver is just outside the Gullet weapon shop. His quest won't be available until after you have completed the Presidio quest for the Frogfather.