If it's regular ammo (that is, not tracer, AP, explosive, etc.) then all is well. Just so long as your mail recipient is allowed to possess ammo (nonfelon, over 18 (21? for handgun ammo?), etc.)
It is also legal to mail-order and receive ammo in Kalifornia. (LA City? County? may have exceptions but I don't think it's enforced and anyway 1st violation is an infraction I think. Also, LA folks can drive to next city or county and buy ammo off shelf without permit, waiting period, etc.
Flying with ammo is no problem - but then I have flown with declared guns too. If you were referring to flying with ammo alone and without accompanying guns, some questions might be raised but nothing bans it.
My gun+ammo+flying experience has been on Alaska Air only (hunter friendly) on west coast.
Check airline's website about prohibited items and sporting goods, and print out and carry with you when time to fly.
Bill Wiese
San Mateo, CA