Flyers are one on the really big additions to 6th edition. More than Allies, Fortifcations or Double FoCs, they are something different and new. All of the previously listed items are in some way, reminiscient of something you've dealt with before. Allies are bringing in armies you've played against before. Fortifications are just static tanks/terrain for all intents and purposes. Double FoCs is just more of the same. Flyers though, are new to 40k and are part of the new focus on list building. The issue is, there often aren't many solutions to flyers.
So let's put this out there, because it seems some people aren't understanding this despite it being said over and over. 6th is in its infancy. We're playtesting as much as we bloody can and we're putting down our initial thoughts after playing with whats happening. THIS IS NOT CANON. If there's no playtesting involved in something, as ever, we say this. I'm sure we will come up with more detailed posts on each army as we learn more or find out somethings we said before were completely wrong. We're all still learning and rather than just staying silent and letting everyone figure it out alone or in their local group, we're providing a great big group think tank. That's why we're also not promoting buying anything, unless you really, really want it, until things settle down. And that might not be for a long time in relation to flyers because rumors keep pointing to a new batch of flyers just round the corner.
Why is this an issue? Because there isn't much anti-flyer currently out there - some armies constructs will probably be invalidated by this as now, you need to be able to hold objectives, be mobile, kill enemy infantry, kill enemy vehicles, be good at shooting to some capacity, have some sort of assault defense (note: MSU is an assault defense still) AND deal with flyers. That extra option can't be shoe-horned into some armies due to points or the army design at 2000 points. The armies which already 'have' anti-flyer weaponry or can morph their design to include are ultimately going to be the most successful. Even if more anti-flyer options are brought in - more Skyfire units, flyers, etc. Armies which can't afford to lose points to grab such units whilst keeping a coherent force elsewise aren't going to benefit from this. The game as a whole will though and it needs to be done sooner rather than later hopefully.
Beyond this though, some armies don't even have the OPTION of dealing with flyers halfway well, even with Allies. The only super reliable anti-flyer options out there are other flyers (specifically, Stormravens, Vendettas & Scythes) and the Hydra which sucks when there are no flyers around, thanks for that terrible ruling Games Workshop. Can't at least Ally of Convience with Imperial Guard, Blood Angels or Necrons? Ouch. And the issue here isn't really the one or two flyers - a normal army with some thought to dealing with flyers can take down such (we'll discuss this in a bit), but rather an army of flyers. Now this isn't to say you should bring an army of flyers, anything more than two Vendettas is just silly, three Stormravens is much more viable but 4+ Night Scythes and a Doom Scythe? That's a fairly decent flying army without sucking up too many points of a 2000 point army. No flyers or straight AA? That's going to be tough to deal with and this is where those rumored flyers will hopefully come in to plug those holes in the Ally chart. There will hopefully be more beyond this, like FAQ'd Skyfire missiles and maybe one other unit per army to be Skyfire (*cough Hive Guard cough*) or flying MCs to combat flyers in some way but that would be a nice first step.
This would most likely mean you'd need to in some form, buy a flyer to combat your opponent's flyers in theory (again, if those extra FAQs come out, not such an issue). Again, this isn't saying run out and buy a flyer pronto, just be prepared that you might need to get one in the future. Unless you really want one right now though, wait. See what Games Workshop does. They may surprise us again!
Dealing with Flyers Currently
So, if you don't have flyers and don't want to take the Hydra, how do you deal with flyers? There are two main processes here - fortifcations and weight of fire (twin-linking optional but preferred). The former is useless without the latter but the latter can work alone. The former is a single emplacement (or two at double FoC 2000 points) and thus targettable by your opponent and thus needs support. If you're not running a Hydra (or other AA post-FAQs, new releases, etc.) or flyers this needs to be high rate of fire units. You should have these regardless as its good in 5th and still is in 6th thanks to hull points. S7+ is best though S6 can work against the lower AV flyers as well - remember there are AV12 flyers out there.
Add onto this the option of twin-linking, through intrinsic or external means, and rolling lots of dice and then re-rolling lots of dice is going to get you a couple six results and you can start pinging off hull points (or get lucky and drop the flyer automatically). This will unfortunately take a lot of firepower not matter what you do and ultimately will allow you to deal with only a couple of flyers (i.e. ~30 TL S7 shots will deal three Hull Points of damage to an AV12 flyer which doesn't jink). It often becomes a case of should I really be dealing with this flyer or should I be sending all that firepower at the rest of my opponent and dropping several other vehicles or infantry models instead. Sometimes, accepting you cannot easily deal with the flyer early in the game as you work to dismantle the opponent's army and then deal with the flyer later is better. But your army needs to have that option in place as well and your opponent will attempt to nullify that firepower if possible.
There are other options which appear to currently work against flyers as well to bypass their zooming mode. Signum is up in the air but could allow one weapon to shoot at BS5. Certain line psychic powers or shots can automatically hit a flyer if they go over their base and some psychic powers can directly deal with flyers through multiple means, etc.
If you cannot therefore deal with the flyer (either you didn't take the required firepower or it got shot down), there are other ways you can manage them. They have a very large footprint and some flyers cannot hover (and if they do hover, they are a lot easier to hit which renders their relatively immunity to firepower null and void) which means they need to go a set distance each turn. Remember your blocking against jump units and skimmers? Same principles apply but now you can pre-measure. They also only get ONE rotation each turn. This isn't going to stop them from shooting at your entire army (unless you're bunched up on one side) and canny movement of the flyer will generally get them shots at decent targets each turn; you can limit it however and particularly limit what they are shooting at. Make sure you keep them away from rear arcs of vehicles or where they could potentially drop units in advantageous positions if they have this option (i.e. on objectives, etc.). Even using such concepts when you do have anti-flyer firepower available isn't a bad option as you're attempting to take away the advantages of the flyers.
More releases are coming, particularly to do with flyers. We'll hopefully see some more FAQ's helping individual armies out to ensure with the new flyers + allies, there are no holes for any army in regarding a couple flyers or even mass flyers. Fingers crossed this won't involve ALWAYS buying a flyer but that might just be the case.
Until then, if you don't have access to a flyer yourself or don't want to use them plus the lone skyfire option out there, combine the use of fortifications with lots of high rate of fire S7+ weaponry to try and keep the skies clear. Twin-linking that firepower is going to be of great assistance but don't always focus all this firepower on the flyers. Doing so can let the rest of your opponent's army simply laze their way across the board and defeat you themselves. Use other options at your disposal to blunt the flyers impact until you can potentially deal with them whilst keeping your opponent's army at bay (i.e. later in the game).