The simplest solution is to put all of the paths in one shape layer, group them, then apply Trim Paths to the group.
If you have multiple layers, you will need to tie each trim path to a slider control on one layer and then calculate the percentage of the total trim assigned to the slider and apply that calculation to the expression for each layer.
For example, if the total path length was X and Path 1 was 30% of the X then the expression for a 5 second total move would look something like this:
t = time;
l = .3 //percent of the total length
mt = 5; // move time in seconds
linear (t, 0, mt * l, 0, 100)
If it were me, I would use the first option unless it is absolutely necessary to have the paths on separate layers.