) Find an African SMS gateway which offers an API to send/receive messages. You could probably make this work with an SMS to email gateway as well, although it would add some complexity.
) Build a web application which acts as a multi-group chat server, where people can join/leave groups and chat to other members of the group. If you're not familiar with the process of building a web app, this will be a lot easier than going straight for the mobile version.
) Add a REST API to this web app, and build an Android/iOS app which connects to the API.
) Add SMS support to the web app. Use control messages (e.g. "/join some_channel") to join/leave groups. Figure out how to route SMS messages to a particular group - when an SMS is received for that group, use the API to send the content to other group members.
This could be implemented with a variety of stacks - personally I would go with Django for the web app, with Redis as a backend. Redis would be great for storing group membership, and I'm sure you could do something interesting with pub/sub for the messaging component.