If i hold both the british LLB degree and US JD are chances of getting H1 visa better?

Yes they will, check out the USCIS a href="http://www.uscis.gov/portal/site/uscis" rel="nofollow"http://www.uscis.gov/portal/site/uscis/a that is for immigration and below is a good read for the fact and what you wish to do. Good luck