Can I get sliding genioplasty without having straight teeth?

Sliding genioplasty moves the bone of the chin forward to change the facial profile.   The shape and position of the teeth do not change.
It is not necessary to align teeth ahead of surgery.   Provided teeth are healthy and there is no gum disease the straightness or otherwise of the teeth is not important.

Thank you for sharing the photos. Yes, certainly. Genioplasty is one of the surgical procedures of the jaw that can be performed completely independent of your occlusion (bite) and will not affect it. It is also one of the procedures that is likely to give you most dramatic results from the aesthetic perspective. The issues highlighted in your photos, namely weak chin, soft tissue ptosis/excess at the chin point and fat deposition under your chin can all be successfully managed irrespective of your bite. And more importantly you are likely to get a much improved results.

The condition of your teeth, particularly in regards to their alignment or occlusal relationship, is irrelevant for undergoing a sliding genioplasty procedure. The bone cuts for this procedure are done below the roots of the anterior teeth and do not affect the occlusion in any way. Thus you may move forward with the surgery at any time.