As I mentioned in my post on callbacks, one way to increase your ability to land a job as a law professorship is to work as a Visiting Assistant Professor (VAP) or to obtain a fellowship aimed at those who wish to transition into the academy. A number of institutions now have such programs (including my law school, Arizona State). Paul Caron (aka TaxProf) does a great job collecting the programs here.
While I have occasionally seen criticism of these programs --- not that the programs themselves aren't helpful, but that it is a big burden on aspiring law professors to take a short term job in a different city often for less pay --- as someone who benefitted greatly from the Climenko Fellowship at Harvard, I think these concerns have been overstated. Accepting a job as a law professor will almost always require a move to a different city and a loss of pay, so I guess I don't see why it is unreasonable to impose that burden for a VAP or fellowship if it is a burden that most candidates will ultimately have to bear . . .