Its more technique than color. Used black, shades of brown, shades of grey, a touch of yellow or white on a sunny edge, etc the use technique to layer paint. If its a dark tree start with a base of something like burnt umber but if its a lighter tree yoy may want to start with a grey shade and if its a white tree like aspen you may wish a very light grey or off white base to build the bark textures on. Bark is many colors and shades if you look close and time of day changes them too so study tree bark to get a visiin in your head.
Figure out what species of tree bark you are painting. Go look at the tree or a picture of it. Not all tree bark looks the same. It can be covered in different colored lichen or moss too. Study your subject.