Their hopes of a medal got a boost as the world champions from New Zealand and the much-fancied Australian pair both failed to qualify.
Grainger, from Glasgow, who also won silvers in the Sydney, Athens and Beijing Olympics, returned to the sport in 2014 after a two-year sabbatical.
She and Thornley failed to make the podium at this year’s European Championships in May, but Grainger hopes Team GB supporters — “the best in the world” — will cheer them on.
“Medals are won by split seconds and that support makes the difference,” she said.