Do I need to wait for my Kybella paralysis to subside in order to have Ultherapy under my chin?

One must wait for complete recovery of the marginal mandibular nerve palsy after Kybella  before embarking on further treatment.
I would highly recommend an ultrasound exam to confirm the location of the fat with respect to platysma. If the fat is below the platysma muscle you will need surgical approach and not Ultherapy. 
One of the rare complications of Ultherapy in that region is also marginal mandibular nerve palsy and therefore see an experienced physician.

Yes it's best to wait to make sure the nerve recovers before you add another treatment to the mix.  Be sure to discuss your goals and concerns with your board certified plastic surgeon and consider the pros and the cons. Be certain your surgeon is properly certified.  I've attached a link where you can start your search. 

I am sorry to hear about your complication after injection of Kybell!I assume it is your lower lip that is not moving normally on one (or both?) sides. I would certainly want to await full recovery of your paralysis before entertaining another treatment such as Ultherapy. This treatment uses high intensity focused ultrasound for its face and neck toning treatments. Theoretically, it could interfer with your body's quest in healing after Kybella treatment. Best of luck