How was decolonization in Africa & Asia related to the American civil rights movement?

These kind of fed into each other -- sort of a two-way street.

Decolonization in Asia generally started to happen before the Civil Rights Movement.  As these Asian countries became independent, they became pawns in the Cold War.  As the US and the USSR competed for those countries' loyalty, civil rights became an embarassment to the US.  US treatment of non-whites made us look bad in the eyes of these new nations.

Decolonization in Africa generally happened around the same time as the Civil Rights Movement.  Africans took heart from the US movement and it helped encourage them to push for independence.  At the same time, African Americans became more aware of and into their African heritage as these nations became independent.