If you apply for a working visa to the US, but will be travelling and applying with your South African passport, must you disclose that you have a British passport as well? It asks the question do you have nationality with another country. I just don't want to complicate things so not sure whether to say yes or no.
Yes, you should absolutely answer questions truthfully on immigration forms.
Giving false answers on an immigration form is a criminal offense. The consequences if your omissions is discovered are much more severe than any problems you will get from admitting dual nationality, and can include revoking your visa and being banned from the US.
It's very unlikely that having British nationality will negatively impact your application. Relations between the US and Britain have improved considerably in the last 200 years, they don't see being British as a negative.