Rhodesia and Nyasaland (1953-1963)
The Federation of Rhodesia and Nyasaland (also known as the Central African Federation) was a British colonial entity consisting of Northern Rhodesia (now Zambia), Southern Rhodesia (now Zimbabwe), and Nyasaland (now Malawi). It was intended to become an independent dominion within the Commonwealth, but Nyasaland and Northern Rhodesia opted to secede, becoming independent states with majority rule shortly thereafter.
Of the three symbols featured on the coat of arms, only the sun (representing Nyasaland) is still in use on a flag. Initially described as a setting sun, it was changed to a rising sun when Malawi became independent in 1964, and since 2010 it has been a fully risen sun.
You can see a photo of a real flag of the federation here.
Zimbabwe Rhodesia (1979)
The unrecognized minority-ruled Republic of Rhodesia transformed itself into a biracial state following the Internal Settlement of 1978. To signify the change in government, they adopted this new flag on 1 June 1979.
To me this design just screams “uneasy truce.” There’s elements that look like they’re from an African flag and elements that look like they’re from a European flag, but they’re all off in their own little corners, separated from each other by a big white field.
Now compare that to the flag of post-apartheid South Africa. The different colours on that flag co-mingle and blend together to make a single unified design which represents the various communities moving forward together into the feature. For my money it’s one of the most successful and beautiful flags in use today.
As for Zimbabwe Rhodesia’s flag, it fell out of use within a year as the territory reverted to British rule in preparation for majority rule and independence. There are some photos of the flag online here and here.