Your FS character did not suddenly find himself on a starship in the role of an officer. Even though you're bringing your character from a fantasy setting suddenly into a sci fi one, as long as that character is in S&S, it's as if he or she has always been in Spacefleet, in this universe and will always be (from the in-game perspective). You could, on a personal level, write this off in an "it was all a dream" capacity, but there's no compulsion to do so or extra hoops to jump through (Article 8 of the FLAILSNAILS conventions). Although you'd have all of the levels and experience earned through normal FS games, we'll just be writing previous adventures off or, even better, slanting them to reflect the "new continuity" (ie, your FS druid, now a medical science officer, remembers his time in the Lost Caverns of Tsojcanth as being on an away mission). These "changes" do not affect the character in any permanent way; they're merely a way to maintain a sense of consistency in what could be an incredibly strange environment.
Your FLAILSNAILS character's stats will remain more or less the same with one major alteration: Wisdom becomes Psionic Potential.
Humans obviously stay humans (but you could be something different if you wanted), but elves can become either Taurans or Andromedans. Dwarves and halflings can either choose to be humans in S&S or pick one of the other races. Half-orcs are tailor-made to become Rigels. Got something else that another FS DM let you play? Talk to me, man, we can work something out. Gnomes should just shoot themselves.
Fighter, ranger and paladin-types usually end up becoming Military officers, and can choose a subclass that they qualify for. Of course, you could go into a different branch of service if you want. If you decide that your 3rd level dwarven fighter needs to be a Gorran Communications officer, no sweat. Sounds great. Let's do that.
Cleric, druid, magic-user, illusionist and similar spellcaster-types usually end up becoming Science officers, but could just as easily become Technical officers. If your character is Tauran or Andromedan, you get psychic powers. If you're human, check with the DM. My hard and fast rule for this would be that if you are converting a spellcaster to S&S and have a Psi Potential (PSI) score of 13 or more, you get to be psychic. That's cool with me, man.
Thief-types usually make great Techinical officers, but could go Science or Military branches without too much brain-stretchery.
Race-as-class and multiclass characters have some decisions to make. Since there's no real multiclassing in S&S, pick a branch that most completely reflects what your character should be doing. Realistically, most folks in this boat, could pick between any of the different service branches (ie, a B/X elf is equal parts spellcaster and fighter with some thiefiness thrown in, so you could go Military, Science or Technical very easily).
All equipment is off the table. You do not get to bring your magic runesword into space with you. The society of the future is a decidedly non-materialistic one, so you pick equipment normally for your mission.
Your character does not need to have a subclass.
Any other conversion issues get decided by the DM, but I think I've covered everything.
If it weren't for consonance, I'd have called this segment "forming the party" or something like that. Anyway, here are some thoughts about how to put together a good crew for your spaceship.
The highest ranking Military Command officer is the commanding officer of the crew. If there's no Command sub-class present, then the highest ranking Military officer is the CO. I don't normally like to put one player in charge," but the game and genre do make distinctions of this sort fairly important. The CO may choose his First Mate, XO or "Number One;" choice of nomenclature is completely up to the group.
A good mix of classes is, as usual a good idea. The players may want to work together as a team to decide what they're bringing to the table to make sure that the away team complements each other well. Same thing with gear; it's a wise idea to work out beforehand who'll be bringing what down to the planet's surface.
You do not need one of each type of subclass. That would be out of control.
There's absolutely nothing wrong with using Trek characters as models. I'd expect captains to ... pause dramatically or get indignant at the manipulation of cosmic imps, Science officers to be hyper-logical or overly-empathic, and Techs to ... be blind or have Scottish accents? Sure why not. Whatever works for you and helps you invoke the pseudo Trek vibe of S&S.
So, that's how I'd do it. It'd be purposefully episodic to account for the variances in crew and such, which would make the game feel a lot like the first season of TOS and exactly what I would want. Like so many of the project ideas I get excited about, this one would have to wait awhile and get put on the back burner for the time being. But, here it is. Maybe it'll happen some day.
Thanks to Zak Smith & Erik Jensen for the inspiration for this idea.