In my experience (which is reasonable) there is a fair amount of freelance work out there, not generally in initial accident investigations for somebody like AAIB, but more likely in post-report "adjustment": advising legal cases as an expert witness, providing input to insurance companies own deliberations, etc.
The best bet is to get yourself registered with somebody like the
BAAC or
RAeS and perhaps make yourself known to one or two of the law firms who are involved in commercial aviation work.
It's also worth mentioning that in this line of work, once one has got past the basic requirement to know an awful lot about your subject, there are other skills you need. The single biggest of these is report writing - if you have, say, an engineering degree or an MBA that should help you a lot but my experience is that the rigour of the sort of reports one needs to be writing in consultancy is rather more than in most undergraduate level work - closer to PhD level. Of course, you don't need to have a PhD to be at that level of ability, but you do need a lot of experience of writing big complex technical reports for an aggressively rigorous readership.
G