The free ship token system is a little buggy. I've had issues with it myself in the past and spoken to many others on ESD(Earth Space Dock) whom also have had the issue you are having. Its a simple work around to correct it, assuming you have followed the correct steps to acquire the ship token.
Receive your promotion from Admiral Quinn (assuming he is in his officer and not at the club drinking)(bug)
Go down the turbo lift to the ship requisition officer and speak to her (can't remember her name) this should finish the new ship mission Quinn just gave you and award the token. Its not a physical item so you will not see it in your inventory.
Exit out of conversation with her. This is where the bug is. Sometimes if you remain in the conversation and go directly into the store to purchase a new ship it will not register the free ship token. Sometimes it will. Its a bug. Best to just exit the conversation, then talk to her again and go into the store again. If this still doesn't work, sometimes it helps to click on a few different ships or change the search options around to trigger the tokens appearance.
Get a new ship, name it, register it, outfit it, make it look pretty, and go blow something up.
I hope this helps anyone having this issue, as I said its a simple bug that I run into almost every time I get a new ship.