Work

Now I'm aware that Spira doesn't have much normal work except for sales clerks and so on, and Rikku certainly hasn't done anything like that in her life (I wouldn't think so, anyway...). But there is much that she has been during her life and I have listed her roles/jobs here.

daughter of Cid

I know this is not an official job or anything, but I would think that being the daughter of the Al Bhed who brought the race together requires some sort of work ethic. Especially since this is Cid we're talking about.
There must have been some PR'ing to do when they build Home and Rikku obviously must have done some part of it. Al Bhed know her (pretty much by sight) and it takes some work to keep up the good morale and keep them following Cid. Oh, and she was trusted to kidnap Yuna, so she must be of some value to the Al Bhed, no?
Sort of like the princesses we have in many European countries. They do not actually do much when they're young, but they do a lot of work to keep up appearances and such. Although I have a hard time figuring out why Rikku would care for appearances. She's the 'if you don't like this, then sod off' -type of girl.

guardian

Ah, now we get to the real work. Although this is more like volunteer work to guard the ones you love. Rikku is Yuna's guardian and it can be viewed as a real job, just like celebrities' bodyguards, except they guard summoners. And against real monsters, not just overly hyper fans who want an autograph.
Anyway, Yuna has a lot of guardians. She trusts many people, it seems (don't know if this speaks good about the people or bad about Yuna's sense of judgement). Good thing Rikku is one of them.

Gullwings

It's main headquarters are in the Celsius, an airship that Buddy and Brother found in the far north. They thought they were done for, and miraculously a Gull appeared and led them to the airship. That's why the group's called Gullwings.

Shinra is the brains of the group, who invents all kinds of stuff. Good for the Friendly Neighborhood Gullwings' business.
Buddy is Brother's friend, who pilots the airship and reports any distress signals. He's pretty sane, too.
And Brother. Rikku's brother and the so-called "real leader" of the Gullwings. Like anyone listens to him. He has a major crush on Yuna, and wants to see her dance all the time. Oh, and he pilots. Although most of the time he's boosting over being a leader or dancing.
Gullwings also houses YRP, which in short is a group formed by Yuna, Rikku and Paine. I don't really know WHY they have this little group....to appear cool?

Gullwings are a lot of different things during the game. First they're Sphere Hunters fighting against LeBlanc, then on chapter 3 they get turned into "Friendly Neighborhood Gullwings", who charge for taking care of fiend problems. You see Buddy negotiating prices on several occasions, but Yuna's gil stash just doesn't seem to grow....Towards the end of the story, Yuna takes on her responsibility as high summoner and Spira's guardian, and saves the world from Shuyin and Vegnagun.