Flying-types are my 5th favorite Type, and actually, in the earlier Generations of Games, I had more Flying-types on my Team than Dragon-types, due to the fact that Dragonite and it's pre-Evolved forms were originally the only Dragon-types.
(I, like Lance, used Pokémon such as Gyarados and Aerodactyl, which are actually Flying-types, despite being "Dragons".)

1. "It is the Δ, born of the great disturbances in this world."

I already covered how powerful Delta Stream is in my Dragon Master Blog, but since it affects ALL Flying-types, and not just Dragons, I thought I should go into more detail, here.

First of all, Delta Stream negates ALL of the defensive weaknesses of the Flying-type, without actually removing their Flying-type status.

This essentially means that many Flying-types (including all of those Normal/Flying-types) have NO Type weaknesses, as long as Delta Stream is in effect.
(Similar to Sableye and Spiritomb, pre-Gen 6.)

Obviously, this can be quite powerful, especially if used in Triple Battles, and for anyone using an all Flying-type Team, it's DEFINITELY worth having a Mega Rayquaza on it, provided that it's one that includes Major Legendaries.

It should also be noted here that there are MANY powerful Flying-type Legendary/Mythical Pokémon, such as Lugia, Ho-oh, Yveltal, and Arceus (Flying Forme), all of which can GREATLY benefit from Delta Stream.

2. Offensive Weaknesses

The way Flying-type Moves should be viewed, is essentially as an improved version of Normal-type Moves (much like Dragon-type Moves once were), as most of their weaknesses are the same.

Like with Normal-type Moves, Rock and Steel-types are a concern, although rather than being unable to hit Ghosts, you need to worry about Electric-types, instead.

How do you do this?

Well, unless your particular Flying-type can learn a Fighting or Ground-type Move, this can be somewhat difficult, as Bird Pokémon (by which I mean all Flying-types which resemble Birds) typically don't get a wide variety of attack Types.

Usually they can get Steel Wing, which covers Rock-types, but finding a way of dealing with Steel-types is usually much harder.

Basically, your best bet is to have some Flying-types that CAN learn a wider variety of Move Types, such as those Birds that AREN'T Normal/Flying-type, like Pelipper, Honchkrow, Altaria, etc.

3. Defensive Weaknesses

If you're not using a Mega Rayquaza, this is a MAJOR concern, especially considering many Flying-types aren't that defensive in nature.

As always, the best ways of addressing this are having a wide variety of secondary Types, and using defensive Berries and other Items.

One thing that should always be considered with Flying-types, however, is the Move Tailwind, which doubles your Team's Speed for 4 Turns.

Flying-types usually are heavily dependent on being fast, so teaching one (preferably a sturdier one) Tailwind is DEFINITELY a good idea, and can be quite handy, especially in Double/Triple Battles.

Also, the Move Roost removes your Flying-type status for 1 Turn, and aside from making the user vulnerable to Ground-type Moves for 1 Turn, it ALSO negates the Flying-type's weaknesses for a Turn, as well.

4. Flying-type Moves

In Gen 5, Acrobatics is THE best Flying-type Move, especially when combined with a Flying Gem (which increases it's effective Power to 165, not counting the 1.5× Power boost it gets if used by a Flying-type).

Unfortunately, this technique doesn't work in any other Generations, so what Moves should you use?

Well, Acrobatics IS stiil a good Move, provided it's used by a fast Pokémon with a high Atk Stat (and no Held Item, of course).

Also, Fly is always a good Move, and can be learned by most Flying-types, as well.
(You'll need to be careful about how you use it, however.)

Drill Peck and Brave Bird are good Moves, and are arguably better than Fly, for those who can learn them.

Aerial Ace is pretty weak compared to other Flying-type Moves now, and IMHO, should only be used if your Pokémon has the Ability Technician, which raises it's Power by 1.5×.
(There ARE times when it's useful, though.)

Bounce can be a good Move for certain Flying-types as well (such as Gyarados), although not many of them can learn it.

Sky Attack, as powerful as it is, should ONLY be used in conjunction with either a Power Herb, or a Flyinium Z, as it's just WAY too dangerous to be sitting around doing nothing for a Turn.
(I DEFINITELY recommend using it, however.)

As for Special Flying-type Moves, Air Slash is usually best (when it's an option), but Air Cutter, while pretty weak, CAN be a decent Move, IF used correctly.

Also, Hurricane is an AWESOME Move, although it's pretty inaccurate.

This can be addressed, however, by either using Rainy Weather, or by using Accuracy increasing Items (like Wide Lens and Zoom Lens), Moves (like Hone Claws), and/or Abilities (like Vivillon's Compound Eyes, or Mega Pidgeot's No Guard), which can negate this.