Speed of light travel

But then the speed of light is universal constant regardless of the motion of its frame of reference, so shouldn't their relative velocity be $c$? What is their relative velocity and how?

EDIT Upon further review (special thanks to Alfred's comment), I think my original answer is incorrect. It turns out that the question of relative velocities of photons moving in the same direction is a meaningless question. The reason is as follows.

For two objects A and B moving as such,

                       v
               u      -------> A
            -------> B
            ------------------ (ground)

The velocity of B in A's frame is then $$ u'=\frac{u-v}{1-\frac{uv}{c^2}} $$ Notice the denominator? For $u=v=c$, this is zero and we get 0/0 which is an undefined operation, hence the meaningless question.

Do objects moving at the speed of light obey law of addition of velocities?

Not exactly. The Galilean velocity addition, $s=u+v$ does not hold for large-velocity objects. We use the "composition law", $$ s=\frac{u\pm v}{1\pm\frac{uv}{c^2}} $$ where $\pm$ depends on directions/frames. If $uv\ll c^2$, then this does reduce to the Galilean transformation.