There is a sort of relationship between velocity and gravitational time dilation, but it is the escape velocity at a given radius that is required. The Newtonian escape velocity is:
LaTeX Code: v_e = \\sqrt\\frac{2GM}{R}}
See http://en.wikipedia.org/wiki/Escape_velocity
This is the velocity attained by a particle initially at rest at infinity (loosely speaking) when it falls to a radius R as its potential energy is converted to kinetic energy. Inserting this velocity into the SR time dilation equation gives:
LaTeX Code: T singlequote/ T = \\sqrt{1\\frac{v_e^2}{c^2}} = \\sqrt{1\\frac{2GM}{Rc^2}}
This is the time dilation ratio of a particle hovering at R. For a particle orbiting at R you have to multiply gravitational time dilation at R by the time dilation due the local orbital velocity of the particle.

I don't see how we can relate velocity and gravitational time dilation of an observer moving along the r direction in a gravitational field by using the definition of proper time from special relativity.
If an observer moves along the r direction the Schwarzschild metric reduces to (spherical symmetry):
[tex]
ds^2=(1\frac{r_s}{r})c^2dt^2\frac{dr^2}{1\frac{r_s}{r}}
[/tex]
which would yield:
[tex]
d\tau=\sqrt{\left(1\frac{r_s}{r}\right)\left(1\frac{r_s}{r}\right)^{1} \left(\frac{v}{c}\right)^2}dt
[/tex]