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No, you do not need an ESTA. In this context, "transit" means travelling from country A to country B with a stop in the USA on the way. You are already in the USA and are not intending to enter or leave, so your flight is a domestic flight. The ESTA and VWP rules do not apply.
As a domestic flight passenger, you will not encounter US Customs and Border Protection officers. You will still have to pass through airport security (TSA), but that applies to all flights and they do not deal with visa issues at all.