A yoke is a type of physical restraint put on a farm animal to get it to pull a plow for tilling land. After seeing Will's post about the Bible verse, it seems the doctor is using it as a metaphor for freeing yourself through religion. Before I had seen Will's post, I would have guessed that it was referring a to a similar type of restraint that enslaved people were sometimes forced to wear as a punishment. But now, I'm not sure this other meaning is applicable.

I live in the United States and Black people have had to struggle here ever since slavery became illegal, because even after that they weren’t given the same economic and job opportunities. So I believe, since this man became a doctor and “overcame” the struggle of being Black in a place that doesn’t help Black people succeed, he is talking to other young Black people saying if you want to succeed, you have to work twice as hard and not submit to the culture that wants to keep you low on the social class. That is the yoke, or the burden, they have to work to overcome - to not be lazy or complacent because they will need to work much harder than someone who isn’t Black to get ahead in life.

refers to (and you need to get context from) biblical verse from matthew: "Lord, inflame my heart with love for you and for your ways and help me to exchange the yoke of rebellion for the yoke of submission to your holy and loving​ ..."

A ‘yoke’ here is just something that restricts you and holds you back. The speaker believes that those two things are ‘submission’ and ‘slothfulness’. This attitude is traditional but would be highly controversial in some circles, especially today. Instead of seeing some kind of outside oppression as the yoke, he sees the attitude of the individual himself as being the most important factor determining success. In other words, he was saying that if people assert their own will and work hard, they will succeed. It seems that the speaker attributes his own success (becoming a doctor) to those traits of his.