In most fields, freelancers generally got their experience working for the man, I would imagine that would be the case here...you would need to spend years as an NTSB investigator, and make a name for yourself. Investigators have a variety of educational backgrounds, engineering being common for obvious reasons.

In my experience, freelance investigators of pretty much anything are not hired primarily for their investigative skills...they are are hired for their persuasive skills while testifying in a courtroom. You would need to have the gift of gab, and a high degree of "flexibility" at interpreting the facts in favor of your client.

The client does not usually hire a freelancer to find out what happened. The client already knows what his desired outcome would be...and freelancers who do not have a reputation for backing up their clients probably don't get a lot of work.

If you want to investigate accidents with minimal interference or ethical conflicts, work for the NTSB.