The reavers don't just accept anyone, no. There is a reason for that since certain people join factions just to shoot things rather than flying characters and being there for the actual factions.
Get a good story and a interesting character, proper reasoning of why one character would join a mercenary corporation.
Mary Sue, Revenge, They took my job, they killed my family, they fired me, etc
They are all used rather often, if you think out the box and invest some time, you will most likely be accepted.
But it's not my faction anymore, so give the recruitment a shot, if you don't make it and still just want to shoot, go ahead and join the flares. Because so far I haven't see any interesting biographies of any Flares.
it's kind of outdated, but I'm not leading the Reavers anymore so it's not really my choir to keep everything rolling. I was only putting up some words and counters against the flares due to, from the outside, seemed like a true lack of any originality in the faction.