“Because of their parallel, unpleasant personalities”
 
well that’s bullshit. Just wanted to say that. But most people know that already (maybe they just have friends with different personalities).  
Anyway some more flashbacks is needed. We don’t know enough about their backstory but Matta’s option is the most plausible.

It seems feasible that Fluttershy and Dash began their friendship shortly after gaining their Cutie Marks, but were not super close until a few years later. Until then, they probably exchanged short banter as they passed each other between activities in Flight Camp, and no doubt spent a few hours every week or so just being in each other’s company.
 
While all this was going on, Dash was closer friends with Gilda. Fluttershy was kinda scared of the Gryphon, so she simply avoided her and let Dash spend time with Gilda without complaint. I’d say that it was shortly after Gilda left the picture that Fluttershy and Dash started becoming close friends, some years after the hype of the Sonic Rainboom had died down, and with a good few dozen failed attempts at recreating it encouraging Dash to keep the accomplishment on the down-low.
 
When it came to going their separate ways, I personally believe Fluttershy moved to the quiet life in Ponyville, and that it was no accident that Dash got a job in Ponyville as a weather pony. By then, I reckon, she realised that she needed a familiar face in her adult life, and Fluttershy had been a very good friend to her.

Maybe they were the only ones willing to hang out with each other. We know Fluttershy was unpopular in Flight School, and seeing as the same bullies still hassled Rainbow Dash even after she performed the Rainboom, Dash couldn’t have been that popular either.
 
Gilda and Fluttershy both befriend Dash because all three are unpopular, but while Gilda connects to Dash because of their parallel, unpleasant personalities, Fluttershy sees Dash’s inner good.

Dash was more or less focused with beating the boys in the race. I don’t think she could have ever seen Fluttershy tumble out of the sky.

Regardless of their friendship status at the time, you’d think that they’d catch up with each other the next time they met, including “whoa hey, you got your cutie mark” and “hey flutters, did you know I just pulled off a feat that was thought to be a myth?”

Who is to say that they were friends at that point in time? Whether they liked it or not, both ponies would’ve known eachother’s names at least through their individual reputations. Dash would’ve been gossiped about because she’s competitive, confrontational, and had a habit of crashing. Flutters would’ve been gossiped about because of her height, weak flying, and how easy it was in general to bully her. Basically every pony except Dash bullied Fluttershy at Flight Camp, so it’s likely that they became friends sometime after Dash’s penultimate race out of a need for somepony nice to be there for them.

>old friends  
>Rainbow Dash was apparently unconcerned when Fluttershy nearly fell to her death  
>in turn, Fluttershy was completely unaware of the results of that fateful race  
lol plothole

To be honest, looking at Rainbow’s interactions with the others, I suspect Fluttershy and Gilda were about the only friends she really had. She’s got a friendly rivalry with Appelejack, but other than that? We really haven’t seen her have much social interaction; she actively avoided Pinkie at the beginning of Griffon the Brush Off, and I rather doubt she had much to do with Rarity. Fluttershy probably had the patience to deal with Rainbow’s occasional moments of being a jerk, and Rainbow looks out for her because she likes having someone around who she won’t piss off enough to snap at her.

I really do wonder what their story is. There’s no way that Dash and Fluttershy’s life stories have very little connecting them. Something made them friends, and something kept them as friends, and something made it certain that Dash would always ensure Fluttershy is alright and that Fluttershy would always back Dash up.
 
I don’t know about you, but I think it speaks volumes that Dash, the fastest and most agile flier out there, considers Fluttershy, a weak flier, to be her wingmare/wingman of sorts for anything from catching Spike and Rarity from falling, to chasing down Applejack.
 
Some will say it’s a matter of convenience, after all, Fluttershy is the only other Pegasus in the group. But I just get the impression that Dash genuinely considers Fluttershy to be very capable and reliable in emergencies, and trusts her.

^  
Well the rest can easily take care of themselves. Fluttershy sometimes needs assistance and Dash likes helping others.  
Good girl she is but her tough girl façade makes her be a bit misunderstood sometimes (fans and ponies alike). I know this kind of friends. If you know them well you love them the same as “obviously nice” people.

She sticks up for Fluttershy a lot, even when Fluttershy doesn’t need it.
 
It’s kinda funny when you see how Dash just puts that little extra effort in to being nice to Fluttershy compared to the other ponies Dash knows.
 
There must a very interesting history between them, since they both have probably been friends far longer than any of the other members of the Mane Six.

^Yeah, Rainbow’s kind of a jerk, but she’s still basically a good person. She’s just a socially awkward extrovert, which makes people see her as a total asshole.

*Really want to drink cider  
*wakes up her friend and puts her ahead in line
 
Good Guy Dashie

You disgust me, Fluttershy.