First of all. You have to be extremely careful when dyeing wool, as it will shrink in the water and too much agitation will cause it to felt (i.e. turn into felt). If the kilt has a lining, you risk the wool shrinking as well as the hair canvas in the lining, while the twill cotton lining remains the same size. So you can see this is wrought with problems.

If you must dye your wool, you would want to do it on the gentle cycle with a cup of vinegar. The acid in the vinegar helps the dye attach to the wool. You will also need to dry the wool flat. No matter what, don't use a dryer.