I have had a Form 6 for many years for each overseas meeting I attend. A few points of clarification.
First, the Form 6 listing in Column c requires a description of the cartridge. I use Ball, and Blank and the ATF is satisfied. If you put AP or Tracer or any of the loads in Paul Smiths note above, they will disapprove the permit. I tried some years ago to get them to approve 1 or 2 AP loads and they said NO! This has evolved over the years, but I don’t believe the ATF will issue a Form 6 for these rounds.
The ATF never restricts ammunition or any other hazardous material from an aircraft, they only identify what they think is a problem to the Airline and it is the airline who makes the decision. The airline can fly more than 5kg of ammo in a bag or fly anything else they want to. Alaska Airlines has, or had, an ammo limit per bag way above 5kg.
Tracers, flares, and other pyrotechnic loads are always banned from aircraft baggage.
Ammo must be packed in ammo boxes appropriate to the ammunition. They, the ATF, don’t really like paper wrappers like old 303 and the paper wrapped more modern Soviet ammo unless they are in a cardboard or similar box, but sometimes they will let them go. I unwrap these and put the rounds into plastic ammo boxes. They really don’t like ammo that is loose, and that is exactly what they consider a couple of rifle rounds in a 9mm box. That is why I travel with a series of empty plastic ammo boxes in various sizes from 5.56 rifle and up for rifle and 9mm and up for pistol and a box for 12ga rounds, along with a roll of toilet paper. I have found the ATF and airlines are pretty comfortable with a 25ACP round wrapped in paper that is tight in a 9mm box or a wrapped 40S&W in a 45ACP box or even a wrapped 357Mag in a 5.56mm box, but these rounds better not rattle around. Again, it isn’t the ATF that says “NO” it is the Airline, but if the ATF is happy, the airline isn’t involved. I always put rubber bands around all my boxes so the rounds won’t come loose when the baggage is handled. Loose ammo in a suitcase does attract the ATFs attention. In my experience these same rules apply at most European airports. Typically the airlines scans the bags and calls the police to check them. Anything either of them consider loose will attract attention. In Europe I have had airlines weigh my ammo to make sure it was 5kg. When they do this they insist that the packing is part of the 5kg, and in one case I had to turn over a few rounds of ammo to the police to make my weight limit.
I recommend that when you check in you have a wife or friend there so if there is a problem you can have them take the ammo home. If the airline does seize the ammo (happened to me once with ATF), the Airlines hazardous materials office will typically hold it for a week or so for you or your agent to reclaim it.
Hope this helps!