Most every class that has a Bloodline has a "levels stack for determining effects and abilities" clause.
The Eldritch Scion archetype functions as a Bloodrager bloodline, and therefore uses its rules. The Bloodrager feature states that the bloodlines from other classes must be the same, which means it's all of the same pool.
So, you'd have features of an X level Bloodrager, Y level Magus, and Z level Dragon Disciple. You'd combine all of those levels to determine the effects of your singular bloodline.
There is actually no mention of the bloodline levels stacking, so you would use whichever level is higher and stack the Dragon Disciple levels with that level. Note that Sorcerer and Bloodrager bloodline levels don't stack either even though the bloodline types for them are also required to be the same.
I agree that the Bloodrager and Magus don't stack. Neither class says they do, and without that, they don't.
They do have to be the same, but that doesn't by itself let them stack.
An eldritch scion’s effective bloodrager level for his bloodline abilities is equal to his eldritch scion level.
so magus 10 bloodrager 10 would have an effective bloodrager level of 20 for bloodline powers
effective levels and actual levels don't stack unless they specifically call out that they do.