Fluttershy and Rarity have always had a very distinct and unique interaction, and I do adore it like mad. While it doesn't have the shipping quality of Rarity and AJ, it has something a lot more meaningful and tangible in the show, with Rarity understanding a level of Flutters most of the Mane 4 outside of those two know. Rarity has shown to be quite friendly and gentle with Flutters, something not even Rainbow Dash or Twilight has done, and while Pinkie and AJ have had moments of connection with her they've also had... Not so good moments... Rarity however, while having a miscommunication with Flutters in "Green Isn't Your Color" has never felt particularly mean-spirited to Flutters. Unfortunately, we don't have as much dynamic of Flutters to Rarity, except for the fact that Flutters' natural grace and demeanor make for quite the pairing with an up-front and out-going fashion designer, and Flutters has been shown to have knowledge of the fashion industry to a degree, despite that somehow still leading to a complete flop on her dress (seriously how did that one happen!? She was the only one other than Rarity who knew what was going on!)
Then Rainbow Dash and Pinkie Pie, simply put they have the most energy and enthusiasm, and have been shown to care for one another quite deeply. Pinkie was instantly worried about RD when the latter went to the Wonderbolt Academy, and has been shown to be very in-tune to RD's feeling (without the backlash). RD, on the other hand, has come to understand Pinkie better than most of the other ponies do, at least to me it seems she does. RD definitely cares about Pinkie and the pink pone's emotions, and certainly has the energy and enthusiasm to keep up with Mistress of the 4th Wall.
Twi and AJ... Eh, I dunno, I do agree with what other's have said about it but I've never thought about it truly... I guess a powerful magical user combined with the knowledge and will-power of best orange earth pony with apples on her flank and a cowboy hat on her head that is canon and part of the Mane 6 (HA NOW YOU CAN'T COMPLAIN ABOUT ME NOT LIKING ONE RANDOM BG PONY FROM A SINGLE SCENE IN A RANDOM EPISODE I DON'T REMEMBER! >: D) would make a lot of sense, but... Yeah, never thought about it before to be honest...