What is the damage return type of blademail? Does it matches the type of the damage source or has a fixed damage type(chaos,hero, magical or pure)?
The damage returned is pure type. The amount of damage applied is the same as the enemy hero actually took.
The pure type means you can block damage from blade mail with a Black King Bar
What are pure damage :
From the Dota2 Wiki
The damage return is Pure.
The amount of damage returned is what you received after armor and magic resistance is calculated.