I'm really not a fan of buddlea, and... If you do a bit of research, you might decide to grow something else.
But.... I've never had any difficulty rooting it in clay.
In my experience, any time I pruned it back, I could insert the cuttings into the clay soil and it would grow.... No hormones or special treatment necessary.
But.... I would probably wait until feb or march, when you cut it back to promote fast spring growth.
Buddlea doesnt grow in my sand due to the dryness, and the nematodes, but vitex grows fine, and it roots just as easily.