There is a walking route using lanes and public footpaths - they are shown on multimap.com (you have to zoom in to see them). It looks about 6 miles? That might be OK the 1st morning, but I wouldn't fancy walking back afterwards and then flying home.
I would not reccommend walking along the new bypass that links Turweston to Silverstone, although you do see people doing it.
I usually drive up Thursday night, pitch the tent at Whittlebury Golf club (right next door to the circuit with its own gate) and pack up again on Sunday night to come home. Unfortunately that doesn't help with your fly-in plan
TG.