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. 

Hello and thanks for posting.
There is no question that you should wait until the muscle weakness completely resolves before you have an Ultherapy treatment. One of the potential complications of Ultherapy is also injuring the marginal mandibular nerve which is presumably what happened after your Kybella session.  This is a rare complication after Ultherapy, but the practitioner needs to know your history and carefully avoid a “replay” of this problem.

Good luck!