how to wrap/weatherproof corner when replacing corner trim
Traditionally you'd have just caulked the siding to the corner board, and that would act as the drain plane. However, modern standards do tend to provide a secondary plan, as you've surmised. 

You should be able to gently pry the siding out from the wall just enough to slide any flashing you like in there. Use a flatbar or a chisel, and align the tool as closely as possible to the siding nails. It might also work to drive wood shims in behind at those locations.