It is possible but you'll be competing against people with doctorates in Philosophy and dissertations and publications in philosophical journals.
Usually the requirement for faculty at colleges and university is the "terminal degree in the field." For law professors, this is the JD. For studio artists, the MFA. And most other faculty, the PhD.
I don't think the Provost would raise any issues with your hiring in terms of credentials, but the more difficult thing will be to convince the hiring committee (consisting of mostly philosophy profs with some other humanists) that you're the right person for the job.
Be prepared to articulate why you'll be capable of not only teaching PHIL101, but PHIL2xx, 3xx, and 4xx. If you're at a university, would you be capable of mentoring PhD students? The assumption will be that you don't have that experience, so the burden of proof will be on you.
Many JDs figure it's just as easy to get the PhD with a few more years of school and emerge with a JD-PhD.
[That[Editorial Aside: That all being said, I think you're a bit nutso. Have you seen the starting salaries for law professors? They are earning $150,000+ in the few few years and often have tenure by their 4th year. If I were you, I'd go into the teaching of law and teach very philosophical law classes.]