The local speed of light, as measured in the coordinates of any inertial observer, is always the same. There is no change during the formation of a black hole.
The coordinate velocity of the speed of light could change during formation of a black hole, depending on what coordinates you're using. This is of little interest, because you can always make a coordinate velocity be whatever you like, by choosing the necessary coordinates. This is true regardless of whether there is a black hole or a gravitational field.