I'm not 100 percent sure but i've only been able to get a combo off of BD if I anti air the opponent. I think the reason it works on akihiko in that vid is invincibility preventing aki from getting tripped immediately. But I've been doing BD antiair,2A,2B,2C,j.BB,j.2B,j.BB,j.2b,j.236D.
As for 2C fatal there are way better combos but to start 2C,5C,236B,j.236A,j.2C,2A,2B,2C,j.BB,j.2B,j.BB,j2B,j.236D is a nice combo to start and get you used to picking up after mirage slash.
After that 2C,5C,236B,j.236A,late A followup,j.2C,2A,2B,2C,j.BB,j.2B,j.BB,j2B,j.236D gets you used to doing late crescent slashes for more damage. You can get alot more damage to get off mirage slash loops but those are good for just starting out and learning them.
Hope I helped