You own nose is probably the best guide - put it close to the kilt first thing in the morning and you will know it is is ready for a bath.

I find that washing the kilt in quite a large amount of water is good - hand washing in the bath or large sink seems to be best.

I use a liquid detergent intended for coloured clothes, and water just slightly warm. Immerse the kilt and swish gently, leave for a few minutes and swish again, repeat until the water does not get any dirtier when swishing. Let the water out and leave the kilt to drain for a couple of minutes, refill with clean water, same temperature, swish - etc as for washing, drain, rinse again, until the water stays clean.

Leave for a while to drain, squeeze gently to remove more water, then you can wrap the kilt in a protective sheet and spin dry it if you can do that safely, or wrap it in towels and press to get the water out, or lay it on a flat airer for a day, turning it a couple of times, then hang it. A kilt is heavy when wet and I can sometimes hear threads breaking if I pick them up still dripping.

Washing a kilt in a small sink puts a lot of wear on it. Washing machines with a 'hand wash' cycle aren't bad, but you need to wash a kilt alone. Even then they will show signs of wear faster than hand washing. The colours usually suffer if a detergent with bleach is used.