Imagine a distant static observer that observes a local static observer's clock at the same place that the massive object is moving. According to the distant observer, the local observer's clock is ticking at a rate that is sqrt(1 - 2 m / r) slower due to gravitational time dilation. Locally SR is valid so the static observer also measures the time of the massive object be kinematically sqrt(1 - (v/c)^2) slower. Since there is no relativity of simultaneity between the static observers, the distant observer will also agree that the rate of time of the moving massive object is sqrt(1 - (v/c)^2) slower than the local clock, while the local clock is sqrt(1 - 2 m / r) slower than the distant observer's own clock, so according to the distant observer that is static to the black hole, the total time dilation of the massive object is sqrt(1 - 2 m / r) sqrt(1 - (v/c)^2), where v is the locally measured speed of the object.