i dont mean to scare you, but my daughters head was the slightest bit flat, so i know it can be a serious issue. remember, if you son is crying from being on his stomach, imagine how it would be if he had to wear a helmet. this is a very common problem, but to suggest the helmet may be needed makes it sound a bit more concerning.
ok, heres what you need to do. i assume its flat on one side? change your changing table and anything like a mobile or other toy so your son will lean towards the other side. in his sleep, make sure he is not laying on the flat side. put him in a sleep positioner on the opposite side . also take note, which side you are feeding him if he is only bottle fed. nursing you switch, but with bottles people tend to favor one side.
and remember, he doesnt need tummy time to fix this problem, he needs not to put any unneeded pressure on the flat side to make it worse. wearing your son in a sling will prevent anymore flattening. there are many other positive benefits as well anyway. the flatness happens from sleeping on one side, but moreso from being in strollers, car seats, swings, bouncy seats. since the flatness is already there, when he relaxes his head, it automatically falls to the flat side making it worse. so if you wear him in a sling, he wont be in that position to make it worse.
i would correct it by adjusting his head when he is in places he must be like sleeping or changing, and use a sling to prevent any reoccurences. you should be able to correct this in a month or 2 if you are perisistent. remember, its not tummy time that prevents flattening, its keeping his head off any surface. good luck to you.
ETA- once it is corrected, be sure to alternate everything like sleep sides, changing tables, ect so it wont occur on the other side.