Tutor/Teacher in English Studies, Ancient Greek, Latin, and Japanese
Rob has it. His speech is on civil rights for blacks, and, since blacks suffered under slavery here in the US, he's using the imagery of chains and manacles to invoke ideas of slavery. MLK is equating segregation and discrimination to slavery; he's saying that the manacles of segregation and the chains of discrimination are just as strong, and just as wrong, as the literal manacles and chains of slavery. His point is that any black discriminated against and segregated is still as good as enslaved.