Well, adobe flash isn't a daw either... Or do you make flash animations?
anyways, FL Studio Mobile would probably be mostly for basic functions and I'm not really sure why in sam hell Image-Line felt the need to put FL on the ipad or itouch, it's basically useless. The greatest thing I can see getting accomplished on it is writing out some chord progressions and melodies in some of the basic included instruments. But like said above, you should probably wait to get a DAW on your computer. Just a run through a ton of DAWs:
FL Studio: The messiest but most commonly used DAW, works great and handles a lot of hardware just fine. The built in plugins are pretty good and useful. There isn't a specific genre that this DAW is good at making, it's sort of all-around, I guess.
Ableton Live: Clean, and the second most used from my experience on youtube
The strong point is performing shows live, but it's really great at making a wide range of genres as well. Built in plugins are a bit better than FL's, but that's what you get for $700.
Logic Pro: Similar to Ableton, but I'm not sure how it's performance live works out. Somebody who has used both (Lav and Flatfish come to mind) can go further in depth. Another difference is that you can only use Logic on a Mac. Windows won't run it.
Cubase: An advanced version of FL, being much cleaner, plugins are slightly better, and handles hardware a bit better (I think). Also offers some functions that FL doesn't have.
Propellerhead Reason: This DAW lives off in its own world, running it's own internal plugins, and up until a certain point, plugins from other worlds (like Native Instrument plugins) couldn't visit Reason. Anyways, Reason is clean and it's built in synths are good, and there's really no need to get 3rd party plugins, so you'll save money. There's also a slight learning curve involved in this DAW.
Reaper: They live off the honor code, so the trial is the free version so you can keep it forever and you just get little pop ups saying "Buy the full version!" every now and then. But it's only $60, so it's cheap. I don't know a whole lot about this DAW though.
Pro Tools: The producers nightmare, according to Lavender Harmony. If you get a light version of this from an audio interface that you purchase, you'd have to try it out yourself, but from what I've heard, it's a nightmare to work with.
Mixcraft: I don't know anything about this DAW, other than it will run EastWest Symphonic Orchestra a whole lot better than Ableton live, lol.
So that's all I know, but now this is going to turn into a DAW discussion. Here, have some threads on DAWs that should help you in picking out a DAW:
Thread 1 Thread 2 Thread 1 should be the most helpful to you. But look through them both.