Question

What are all the shiny-locked Legendaries in Gens 3-6?

Answer 1

Here's a list of all Pokemon that cannot be legally obtained shiny:

Gen II-

Mew.

Gen III-

Celebi.

Gen IV-

Arceus.
Spikey eared Pichu.

Gen V-

Victini.
Reshiram.
Zekrom.
Keldeo.
Meloetta.

Gen VI-

Xerneas
Yveltal
Zygarde
Zapdos
Moltres
Articuno
Diancie

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Source
Hope I helped.
Note - some of these arent legendary or shiny "locked" per say, they just cant be obtained shiny because they are event Pokemon that werent distributed shiny.

Answer 2

In Generations 3 - 6, there are 11 unobtainable shiny Legendary Pokemon.
(Well, if that's what you were trying to ask, anyways...)

These include:

      *Arceus (Event Pokemon)*
      *Celebi (Event Pokemon)*
      *Victini (Coded not to be Shiny in Black/White Games)*
      *Reshiram (Coded not to be shiny in Black/White/B2/W2 games)*
      *Zekrom (Coded not to be shiny in Black/White/B2/W2 games)*
      *Keldeo (Event Pokemon)*
      *Meloetta (Event Pokemon)*
      *Xerneas (Coded not to be shiny in X and Y)*
      *Yvetal (Coded not to be shiny in X and Y)*
      *Zygarde (Coded not to be shiny in X and Y)*
      *Diancie (Event Pokemon)*

                                             **Hope this helped, - Aurora_the_Lucario :3**