Who possessed the most "far-flung" empire in Africa?
Like the previous answer suggested, this question is a bit open ended and ambiguous. I actually read the question as which African country is the strongest. So, my answer will focus only on the countries in African continent.
1. The strongest military is Egypt. For example, they have one of the best air forces in the world. It probably ranks around 10. They have equipment from military makers all over the world, which include the US, China and Russia.
2. If you are talking about economy, South Africa possess the strongest economy with a GDP of 272 billion dollars. They are also the largest exporters of gold, platinum and diamonds. If we change the GDP to per capita, then Mauritius is the wealthiest.
In short, it all means what you mean by "far flung."
The answer to this question depends on how you define "far-flung."
One way to define "far-flung" would be geographically. In other words, you could say that the most far-flung empire would be the one whose parts were farthest from one another. If you use this definition of "far-flung" then Great Britain would be the "winner." Its northernmost colony was Egypt while its southernmost was South Africa, which is as far south as you can go on the continent of Africa.
If you define "far-flung" as having the most different colonies (colonies that are now the most different countries), then the French are the "winners."