I'm not sure how the joint degree thing would work out since you're already in your second year of law school--typically JD-MBAs are for people without law school experience, and they require three years to earn both degrees. This blog http://www.jeremycwilson.com/
may be helpful for general information for you, but you'll have to do some research on JD-MBA programs at the specific schools you're interested in.
Asking for the "normal length" for the process is a little vague--we'll need more information on exactly what you're asking for to give you better answers. Getting a good GMAT score, putting together a resume, planning essays, and lining up recommenders takes time. The process tends to get more efficient the more times you do it...i.e. my Stanford and Berkeley apps consumed a large part of my life for over a month, but my remaining three apps (UCLA, Kellogg, Harvard) were much faster because I had all the fill-in-the-blank information/transcripts/resume handy and I had been through the essay process a few times already.