That's an interesting question. To me creativity is deeply linked to non-linearity, having multiple ways to do things, multiple representations of ideas, reveling in contradictions, defying pattern without annihilating it. In some sense I think you don't need to promote it as much as get out of its way. It is the spirit of life. Or at least half of it. There is generation and destruction, all things that exist long enough for you to give them a name are tensions between opposites. Electrons furiously trying to fly away while the proton sucks them back into their flittering dance, out of the many sperm, an egg chooses one, her favorite, you are surrounded by things you could look at, and yet you choose only some of them... That being said, here are some things that come to mind...
- Have collaborative games available: as in positive sum games, where all players can win if they work together. Some examples of this are group musical improvisation, hacky sack, group art. My friends and I sometimes have a few beers or whatever and get a big art pad out with markers and pencils and all start drawing something. We start out in different parts of the pad, some are more skilled than others but that's not what matters. New people often have to be encouraged, "there's no wrong way to do it", "we're just dreaming together", and after a while the images start to merge, and you can come out with some amazing collages or mosaics or whatever you want to call them and everyone has a piece of it.
- During play time, or whatever time makes sense, play two completely different types of music. We used to play go (a great game that blends creativity and logic) while listening to Indian classical music and Spanish psy-trance music simultaneously. At first its clashing, they are in different keys, styles, tempos, rhythms, but it doesn't matter. Like all things you get used to it, and then there will be moments of magical serendipity where the music comes together perfectly and it feels like an epiphany, God reaching out of the woodwork and tickling you in your bum and then it vanishes, back into the primordial chaos from which it came. All things end, after all.
These are just some suggestions. Perhaps you can use them as soil to fertilize your own ideas, something that works for you and your team. Above all, lead by example rather than by commandment whenever you can, let others see your actions and take pieces of it into their own lives. Creativity is a dish best served un-coerced.