I found an example "sketch" for a sam3s,
but I feel the code is instructive for the Due as well.
I do not expect this to run on a Due.
it shows the dac and adc being driven by a timer, and consuming/producing
arrays of data by using the PMC dma.
for me this solved how to run DAC and ADC in parallel.
http://www.at91.com/component/resource/article/Academy/43-Hands-on/1197-sam3s-ek-phone-demo.html
just use the zip file, the separate pdf is the wrong one.