So, legendaries have one time appearances, and I was wondering though if there are any legendaries where you would have an easier time getting shiny than others.
If I didn't do well explaining, I'll try my best to fix it.
Really this depends on how the legendaries are encountered , so ill make a list from easiest to hardest
Shiny events: Some legendaries, like the beasts given during the thirteenth movie, are automatically shiny
Stationary Legendaries: the guys who sit and wait patiently for you to capture them. By "soft resetting" (saving right before the battle and restarting over and over until you obtain a shiny one). This will likely be an arduous process, but if patient, you're guaranteed a shiny. Examples include heatran and Cresselia, as well as in game event Pokemon
Regular distribution events: regular event legendaries like jirachi and deoxys, like all Pokemon, have a small chance of being shiny, but as these are one time occurrences with "no backsies", the odds are not in your favor.
Roaming pokes: the information for these Pokemon (ie shiny vs not shiny) is determined upon your first encounter, which may not be a battle. For example, in Black/White Tornadus or Thundurus appears around the sixth gym, at which point its data is created. You then have to beat the game, chase it down and battle it to see if it is shiny, and if its not, you can't soft reset (as you always save right after you beat the champion)
Impossible: That's right. Some Pokemon, like reshiram and zekrom, are programmed so that can never be shiny.
Hope this helped.