I travelled to Namibia last year and have booked my flight again for this year to fly with SAA and was given some sound advice from members here.
I turned up at Heathrow with my firearm and ammunition in two separate locked (obviously) cases and declared them on check in.
My phone calls to the airline were met with misinformation and a sense that the staff didn't really know what they were talking about so the guys here who had made the journey were the best source of information.
I looked for my flights via Skyscanner and various other sources and selected the one that suited me in terms of price and duration, the booking company was Travel Trolley.
SAA don't charge for carrying firearms so take that into consideration, you might pay a little more for the flight but you won't get the excess baggage charge as you might from other airlines so it may work out much the same.
Basically I checked in online, travelled to Heathrow and checked in there.
I made it clear to the staff I had firearms and ammunition to declare so they waved me to a check in desk that was empty and I handed over my suitcase. A supervisor was called at she told the clerk to waive the excess baggage charge because it was sporting firearms.
I double checked that everything would be booked straight through to Windhoek and it would remain in transit in Johannesburg and not have to be imported and exported from SA.
They radioed for someone to come and see to my firearms and I said good bye to my suitcase and waited for about 20 mins for the guy to find me and get my FAC checked and he issued me with a receipt, directed me to go through the security and gave me directions to meet him in the Border Force area which I did.
There they checked my firearm and serial number against my licence and issued me with an export permit. The ammunition was given a cursory glance but the woman had seen I was allowed 600 rounds on my licence so it must be ok.

My rifle and ammunition disappeared, once again I checked that it was booked through to my destination.
On arrival in Windhoek the firearms collection point is just as you exit through to collect your bags. A simple check of serial numbers, export permit and a quick form to fill out and I was issued with an import permit for the duration of my stay.
That's about it. Dead easy and as long as you travel right through with SAA you shouldn't have any problems.