From the theory of relativity, if any object is moving with the speed of light or more than the speed of light, then the time stops or seemed to be stopped for that object. That means, that the speed of time for an object moving with the speed of light is zero.
So what will be the speed of time for an object in the space, travelling at a negligible speed(i.e.,zero) or approximately stationary.
The expression "speed of time" doesn't make much sense, since speed is the rate of change of position with time, and "time" doesn't have a position. Hence it doesn't have a speed.
If you want to know the amount of time dilation at a given speed, it is answered by special relativity. $t' = t\gamma $ where $t$ and $t'$ are the amount of time that passes in the two frames, and $$\gamma = \frac{1}{\sqrt{1-v^2/c^2}} $$
At low speeds, $\gamma$ is approximately 1, and at high speeds it approaches $\infty$.
To fit with your notion of the speed of time as being the relative rate of passing of time in the two frames, an expression for the speed of time would be $t/t' = 1/\gamma$, which is close to zero at high speeds, and close to 1 for low speeds.
So the speed of time at low speed is equal to 1.
The speed of time is constant for everyone regardless of the reference frame. If (A) moves with the speed of light he won't notice that time is going slower. But for another person (B) not in the same reference frame, he sees his time is going slower.
