1

The cheapest direct to Africa will probably be to Nairobi.

Alternatively you could get a cheaper flight to southern Europe and go across to north Africa by boat.

Depends where you want to go in Africa really......

2

Ethiopian fly Bangkok to Addis Ababa.

You could also try Emirates,Qatar, Gulf, Etihad and see what they offer.

3

Kenya Airways flies to Bangkok, so if you want a direct flight, they are a good option, and Nairobi is a convenient traffic hub if you want to travel Africa (as is Addis, if you opt for Ethiopian). I agree it is always worth checking the airlines from the gulf countries, especially if you are not in a hurry and the detour/layover does not bother you. Excellen airlines, whether you use Qatar or Emirates (both flying to Nairobi). Now during the Haj the flights might be rather busy as many Africans pilgrims use Addis in particular as a gate to their Mecca flights.

Just a word of warning if you haven´t already found out: for your budget travelling in Africa is far less friendly than in SE Asia. But a fascinating continent nonetheless!

4

When I needed to fly from Africa to Asia, I found many connections where I would have had to fly all the way up to Dubai or even London.
Fortunately, I got a direct flight from Capetown/SA to Kuala Lumpur/Malaysia (with further connection to Bali/Indonesia) at a reasonable price (about 450 $, as far as I remember).
Maybe you could take a cheap flight with Air Asia from BKK to KUL (and Kuala Lumpur is worth a stop-over anyway), and fly to Capetown from there (depending on where in Africa you want to go)?

5

It depends where do you want to go. Nairobi with Kenyan Airways and Addis Abeba with Ethiopian Airlines are two good bets. They also offer connections to other African countries changing planes in their hubs so if you aren't interested in Kenya or Ethiopia, take a look at their webs to see if they offer connections to the country that interests you. To fly changing planes in the Middle east is, as it has been said, another option.

You could take also a look at Air Mauritius out of Kuala Lumpur or some Indian Airports to Mauritius, Air Seychelles has a flight to India (I don't recall to what airport) but I don't know about their fares. Air Austral will start later this month a flight from Bangkok and Chennai to Reunion, you could take a look at their web to see if they have promo fares...

I got a direct flight from Capetown/SA to Kuala Lumpur/Malaysia

Sadly, Malaysian airlines isn't flying that route anymore.

6

Be warned: costs in Africa are much higher than you would believe possible. If the cost of the air ticket is a big issue for you, it is doubtful whether you could afford to do anything interesting once you arrive in Africa.

7

On the costs...depends where you want to go.And what you want to do.

Egypt and Morocco are pretty cheap by world standards for example.