Can I get CoolSculpting if I have Factor V Leiden (single gene)?

Yes. Factor V is not a contraindication to the Coolsculpt treatment. Since Coolsculpt is a non-surgical procedure, this treatment may be the best option for you (versus liposuction, or any other surgically invasive fat reduction surgery). I suggest partnering up with your local service provider to determine if you are the perfect Coolsculpt candidate. 

Coolsculpting should be fine with your Factor V trait.  It does not require and incision or create a wound to heal.  You may bruise a bit.  Be sure to see an experienced practice, preferable a plastic surgeon who can advise you on the best treatment for your problem area.

Yes, you can have Coolsculpting with Factor V def.  In fact, this would potentially be a better option for you than surgical procedures such as liposuction or BodyTite that would have bleeding potential.  You should be evaluated first to see if you are a Coolsculpting candidate of course.