It is not a coincidence. Red yellow and green, as well as an alternate color scheme of red, black and green, are often referred to as the pan-african colors.

From the 1900's to the 1960s, when the majority of colonies on the African continent became independent countries, Pan-African theory was an important intellectual movement, originating in the Caribbean and North America but spreading to African elites.

The specific reason that Red Yellow and Green became symbolically important Pan-African colors is because they are the colors of the Ethiopian flag, and Ethiopia was seen as the sole African state to successfully avoid European colonialism.

The selection of those colors probably got an added push when Ghana became the first European colony in sub-saharan Africa to gain independence under majority rule* in 1957. Kwame Nkrumah, the first Prime Minister of independent Ghana, was deeply attached to Pan-Africanist ideology. As you have already noted, the colors of the flag of Ghana are red, yellow and green, with a black star in the middle.

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^* the caveats "sub-saharan" and "majority rule" are both important. Egypt was granted independence in 1922 (except the canal zone), South Africa gained self-governance in 1931, but majority rule did not occur until 1994. Liberia was created as a colony for American freedmen. Ethiopia technically was part of the Italian East Africa colony from 1935-41, but isn't usually considered a European colony in the same way as most of the rest of the continent was between 1870 and 1975.

Edit- If you want to do some more reading about Pan-african ideology and the anti-colonial struggle, this is a good introduction

Edit 2- ok, that didn't link to the correct page. Check page 236, "kwame nkrumah and pan-africanism"