Do you need to record separate values recorded for every BC node? Or are you looking to sum the fluxes for each BC type over the whole model?
If the latter, save a DAC file when running the model (make sure you save every time step). Open the saved DAC file. Go to the Period Budget tab and export a text file using the button provided.
If you want to analyse specific groups of nodes, you can save these as nodal selections. Change the Domain of Interest (DOI) in the Period Budget tab and export again - this produces a budget history for just those selected nodes.