So this question comes up a lot, and I've found a variety of correct and uncorrect answers, confusing me enough to want to go back and carefully search for definitive Greg quotes. Here's the results of my research. Toa that can definitely fly are:
Fire (if they have a jetpack-shaped Toa Tool to channel the flames down)
Air (but it's highly inefficient unless they have glider-shaped Tools or the like)
Another element that can probably fly is Plasma (same means as Fire, but maybe less subtle control).
One element that has technically flown but only with the aid of the Nui Stone is Water (may enable limited hovering ability normally, but probably only a fall-slowing ability due to limits on how much of their element Toa can normally make under control at one time).
Despite common misconception, Toa of Iron can NOT fly.
Other Toa may be able to effectively slow a fall, and still others may be able to slightly slow a fall, etc.; see the end of this post for more theorizing on that.
6) Can a Toa of Magnetism use his control over magnetism on his armour and make himself fly?
6a) What about a Toa of Iron?
1. If a Toa of Gravity was experienced enough with his element, could he manipulate/bend the gravity around him to achieve flight? The toa I'm writting about is able to and I wanted to see if that was a canon-worthy ability.
3. In B2, why does Vakama ask Nuju to use his telekinesis to lift him up to Makuta, when he could just use his Disk Launcher as a jetpack to fly up?
3) Maybe he didn't want to waste his elemental energy powering the jet pack right before such a big battle
Source. I include this because the question has come up before of whether the jetpack is a Tool channeling his normal element (this confirms it) or a separate power that makes its own fire (this denies that). It also confirms that he can fly with the jetpack, though that is obvious since it was shown in-story.
4.)Can toa tools be used by other toas to chanel their element and or would it still if a toa of fire used Vakama's
4) Yes, Toa can use each other's tools, but Vakama's jetpack would not work for another Toa in the same way.
Source. This one may be irrelevant depending on what he means by "the same way" (if just means it wouldn't make fire, then this is irrelevant, but it could mean that Toa of Water or Air couldn't effectively hover as well as Vakama).
On a more trivial note yall might find helpful, while I'm at it, Vakama's Huna would make jetpack flames invisible too. Source.
[After a question about Lhikan's tool]
3. Would he actually go on water, or would he have some mode of flying like Vakama has his jetpack?
3) Lhikan's tool functions sort of like the Silver Surfer's board
Source. This confirms that Lhikan's Tool had its own Kadin-like Flight power; his Fire element was not involved in that Flight.
2.)Can a toa of air fly/glide without a mask of levitation/glider just useing their elemental powers?
2) Well, Matau flew in 2004-2005 without a Mask of Levitation, but if you don't have some kind of glider wings or tools to help you maneuver, you are basically just going to be buffeted by winds, which isn't a very efficient way to fly.
Source. (I think he means creating a strong wind pointing up, which would logically be difficult to balance on top of without some kind of windcatch.)
I could not find direct information on whether or not a Toa of Psionics could fly, but they almost certainly cannot, because the only power Greg gave them that would have a chance is telekinesis, and it's confirmed that the Mask of Telekinesis cannot be used for flight:
...telekinesis -- Nuju doesn't use his mask to lift himself, he uses it to lift other objects.
Toa of Water can fly, but the only confirmed instance is Tuyet's overpowered fountain method which might only be possible due to the Nui Stone, as it was used as the final example of her using that power the most in Many Deaths. Here's the example:
Before the startled eyes of the Toa of Fire, Tuyet began to rise on a column of water. Higher and higher she climbed, until it seemed like she would be able to touch the stars themselves.
I would presume that normal Toa of Water would just be able to slow a fall with a downward-directed jet of water, and more effectively if they had something like Vakama's jetpack to channel it through properly.
I could not find confirmation that Toa of Plasma can fly. They make more heat than Toa of Fire, so logically they can using the jetpack method as well, and probably faster, though the "superpowered" nature of this heat may actually make them only able to rocket at high speeds, without any slow and careful mode.
For all other Toa, flight should be essentially impossible, although it may be possible for some to more effectively slow a fall than others. I would expect these to include Light (the heat side effect of it), Sonics (which has some limited pushing power), Earth (limited liquid-like behavior projected downward with enough force to mimic a jet) and Plants (by making a big leafy glider ). Possibly Toa of Lightning may be able to direct electricity in a spiral or ring shape to make a limited electromagnetic field, though as far as I can tell nobody ever asked Greg about this.
Also, other Toa could project even solid elements downward at as high a speed as they can, to slightly slow a fall, but there would usually be more effective ways to use solid elements to save yourself from a fall, such as making a curving ramp and a surfboard to slide down it with. These are mainly Stone, Iron, and Ice, though the same could help a Toa of Earth to some extent, and Plants.
Also note, a Nova Blast would provide enough use of any element with enough force to most likely enable flight, technically, but it could NOT be controlled to aim only downward to propel them up like a rocket. Instead, the element goes out in all directions, and with most elements (other than Water, maybe some others like Air), the Toa is killed in the process too. Only normal use of elements would be controlled enough to aim downward, and with most of these other elements the amount limit used at once would not be enough to provide lift.
And no, Toa cannot make platforms of their element, stand on them, and lift the platforms. It's often speculated erroneously that for example Pohatu could make a surfboard out of Stone, and lift that while standing on it, since it's confirmed that Toa of Stone can enable Stone to fly telekinetically (as all Toa of material elements can for their respective element). The problem with this is essentially that Pohatu standing on the rock makes the target and the source of the telekinetic power connected in a loop, like the old cartoon cliche of a character putting their feet on a door and yanking on the doorknob in vain to try to open it -- it can never work, because their feet are pushing the same object their hands are pulling, with the same force, so they cancel out.
I did try to find a quote to confirm that this is impossible, and could not. It seems not to be something anybody thought to ask until the new forum, but the fact that it's never given as a power for elements, and even Toa of Iron who have metal in themselves cannot lift themselves, while flight is given as a special ability for Gravity and Magnetism, clearly debunks the idea.
EDIT: That is now in serious doubt, as a quote has been found from one of the books that seems to depict Pohatu lifting himself by telekinetically lifted rock. See conversation beginning here, with the quote here. A suggested alternate interpretation of the physics is that Toa can convert some of their elemental energy into kinetic energy to achieve telekinesis, but the coding of powers like that of Iron Toa includes some limits that have nothing to do with physics limitations, such as for safety or to avoid being overpowered.
Here's another relevant quote that Torchflare1234 found:
19) Is a Toa of Lightning capable of flight?
Edited by bonesiii, Dec 21 2012 - 02:28 AM.