You can absolutely do Kybella treatments being a Type 1 Diabetic. Kybella dissolves the fat inside the fat cells, and therefore will not interfere with your Insulin or Diabetes in any way.
If your Diabetes is well controlled and you do not have any diabetes relates disseases, then you are at no risks to proceed with Kybella treatment. Make sure to inform your family doctor about your intentions as well to inform your Kybella provider about your condition of being diabetic. Good luck!