There are several reason why FSA could, and should come before OoT.
State of the Triforce;
It seem like there's no general knowlegde about it. Only the Royal Family ( or Zelda ) knows about it, as we see a single Triforce in the end of FSA. What's interesting is that despite the Triforce lack of use in FSA they still want to show it in the ending, with Zelda looking at it. This completely lacks a purpose in FSA, unless they wanted to foreshadow something.
Master Sword;
It's just not there. Which is fine if FSS is before OoT since games after OoT seem to use it all the time ( WW, TP, ALTTP etc. ). I am aware that the MS had a role in FSA according to the text dump. All the more reason to wonder why it was removed.
Lost Wood;
We're show the orgin of the Lost Wood in FSA, from being the Forest of Light. What makes this really interesting becuase of a quote by the Deku Scrub. - "But we're trying to build an underground road that will let us go anywhere..." - Sounds awfully familiar with the Lost Wood in OoT, as it had underground roads which could take you far away.
Ganon;
New Orgin. One could argue that this Ganon can come either after or before OoT equally since there is no previous knowlegde about any Ganon before that ( applies to both OoT and FSA ). However, I would give FSA the egde here since it's a newer game. OoT can't reference FSA. FSA however, can reference OoT. Which it didn't.
Gerudo;
You can laugh at the AT and say that it's ridiculous that the Gerudo and their culture would last the flooding, which is shows in WW/PH. However, it would be biased to say that they were any better off on the CT. Especially since TP perfectly ignored the Gerudo. The only hint of them in TP is Ganondorfs 'band of thieves' as they were described in OoT. It IS possible that they was executed along with Ganondorf in the Arbites Ground, just to explain their lack of presence. I don't see this problem if placing FSA before OoT though, as they had to exist before in order to exist afterwards.
Dark Mirror-Twiligth Mirror;
To be honest, I am not too keen on arguing for this one, because I used to argue against it. All I can say is that wheter or not they're the same isn't a concern if FSA is placed before TP, since the mirror wasn't destoryed in FSA. One must admit though, that there are as many similarities as there are differences.
Oldest Tale;
Last, but not least.
Quote
Aonuma: The GBA Four Swords Zelda is what we’re thinking as the oldest tale in the Zelda timeline. With this one on the GameCube [(FSA)] being a sequel to that, and taking place sometime after that.
Seriously, this is probably the most revealing chunk of evidence that Aonuma has ever expressed ( Aside of the Split ). Ironically, it's also one of the most disregarded evidence. By AT and CT theorist alike. AT theorist ignores it becuase it goes against their timeline in general, as they just has to have every game after WW for a reason that's completely beyond me. CT theorist, or at least most of them, seem to have no problem with placing TMC before OoT, yet they don't follow through FS, which was actually confirmed to be the oldest tale.
If we go by the this timeline TMC-OOT/MM-TP-FS/FSA-ALTTP, then Vaati would first appear, get sealed, then he is suddenly forgotten in OoT and TP until he appear again in FS and then it's Ganon from OoT that's forgotten and everyone knows about Vaati again.
I honestly don't se why TMC-FS/FSA-OoT/MM-TP-ALTTP can't work the same way. TMC happens, and Zelda is aware of him in FS, he gets destoryed and Trident Ganon appear. That Ganon gets sealed in the Four Sword. Now, probably because of the wars that happens inbetween, that Ganon plus Vaati is forgotten before OoT, and a new one is born. OoT Ganon eventually dies in TP. Suddenly we're all set up for ALTTP. Blue Ganon is still sealed, perfectly alive in the Four Sword, just the way Vaati would be in this timeline. TMC-OOT/MM-TP-FS/FSA-ALTTP.
There's also the problem that FSA becomes separted from ALTTP, but I don't see that as a problem since they're still on the same branch ( never flooded ) and any reference to ALTTP in FSA are minor ones, or just the geography. But I think that ALTTP, OoT, TP, FSA all have the same geography so w/e.