Question about Elixirs?

How often Protection Paladin use Prismatic Elixir or Elixir of Deep Earth or Elixir of the Master?

It depends on the tank. Some gear around the Prismatic Elixirs/Mastery ones while others gear around a stam flask. It's really personal preference.

When I tank stuff, I will use the Prismatic/Mastery combo if resistable Magic damage is somewhere above 20% or so of total tank damage taken and if it is what is putting me most at risk of death. I figure, resisted damage taken vs ~ 4% (or less) health from stam flask. If I am using the Mastery elixir, then I generally also adjust my trinkets/food buffs so as not to be too far over CTC.

I believe Theck once worked out some kind of breakeven back in T11 a little more formally, but at some point the prismatic elixir will reduce overall damage taken by more then a stam flask will increase health pool, and that is when I tent to like the elixirs. Yor'sahj in particular is a good example of this. Zon'ozz has heavy magic damage, but he can hit like a truck too as he builds stacks, so a good physical defense is still quite important.

extra resisted % from Prismatic elixir * fraction of resistable damage vs % increase in health from Stam flask.

For MOST fights, unelss I am specifically worried about survivability, I simply take the Guild flask from the Cauldron (Stam) and don't worry about it.