Question

Can you get the three moltres articuno and zapdos in Pokemon black?

Answer 1

No, the only way to get Moltres, Articuno, and Zapdos in Pokemon Black is through trading with a previous game or hacking. There weren't even any events handed out for them during the generation.

List of in game legendaries in Pokemon Black and White: here.

It is possible to catch the three birds in Pokemon Platinum, but you'd still need to trade it to Pokemon Black version.

Answer 2

No, You Can't. Sorry :(

The only Way to get Them is by Transferring them From Pokemon Platinum, Heart Gold or Soul Silver to Black. If you Don't have Platinum, Heart Gold or Soul Silver then You'll have to do these 4 Things:

1. You'll have to have to get A copy of Pokemon Fire Red or Leaf Green and catch them on that game. Articuno is located at the Seafoam Islands, Zapdos is at the Power Plant and Moltres is at the Peak of Mt. Ember on Three Island.

2. You'll have to have a Copy of Pokemon Diamond or Pearl and transfer the From Fire Red or Leaf Green via Pal Park. NOTE: You'll have to beat the Elite 4, Cynthia and Complete the Sinnoh Pokedex.

3. Have a Nintendo DS Lite with a Game Boy Cartridge Slot in Order to Transfer From Fire Red or Leaf Green to Diamond or Pearl.

4. Have another DS or 3DS to Transfer From Diamond or Pearl to Black or White via Poke Transfer. In order to have access to Poke transfer. You have to Beat B/W's Elite 4 It's Located around Route 15.

Soure: Experience
Hope this helps :)