The types for the new versions for the legendary birds are:

-Articuno: Psychic / Ice
-Zapdos: Fighting / Electric
-Moltres: Dark / Fire

The types for the new Regis are:

-Regi1: Electric
-Regi2: Fire

There is a secret Regi that is hinted in the DLC but isnt available in the game

This third Regi is Poison type, making all three of them weak to ground, i guess this is a reference to how the original Regis were all weak to the Fighting type

The third Regi will be obtainable in the next game using both Electric and Fire Regis as "keys" to enter a temple where it is sleeping

This third Regi will replace Regigigas