The Legendary Birds (Pre-Elite Four)
The legendary birds are handled as Method 1 Pokémon, but the PID/IVs for all three of them are created at one time using 15 RNG Calls. 1-4 create Moltres, 6-9 create Zapdos, and 11-14 create Articuno. Please note that all RNG advancement must be done immediately before releasing the birds, as it at that time when the Nature and IVs are created.
Moltres
Frame: 1
Zapdos
Frame: 6
Articuno
Frame: 11
The Legendary Birds (Post E4)
Once you have beaten the Elite Four you may speak with Professor Oak and he will re-release any birds which have not already been captured. The remaining birds will be regenerated in the same order as they were originally (Moltres, Zapdos, and Articuno). If none were captured they will appear on Frames 1, 6, and 11. If one was captured the remaining birds will appear on Frames 1 and 6. If two were captured the remaining bird will appear on Frame 1.