Australia declared overnight at 4-322 in the opening game of their Ashes tour.
Michael Clarke set Kent a target of 550, but the four-day fixture in Canterbury became a glorified practice session long ago.
Ryan Harris will be seeking quick wickets to enhance his case for an Ashes recall in Cardiff, where the series starts on July 8.
Mitch Marsh heaped further pressure on Shane Watson with an aggressive century on day three.
Clarke reshuffled his batting order for the second innings, promoting himself, Watson and Marsh up the order.
Clarke opened alongside Chris Rogers after the visitors rolled Kent for 280, but fell for 47 as Australia built a lead of 549 runs at stumps on day three.
Watson crafted a score of 81 and it wasn’t as if the temporary first drop played poorly until picking out substitute Sam Weller in the deep.
The 34-year-old’s problem – aside from the niggle that prevented him from bowling in this game – is that he was overshadowed by the other all-rounder in Australia’s 17-man squad.
Marsh smacked a terrific ton that rocketed the tourists to a total of 4-322 at stumps.
He belted five sixes and 12 fours – all but one of the boundaries coming after tea as the right-hander helped himself to 93 runs off 64 balls.
To put the rampage in perspective, Marsh reached triple figures by scoring 77 runs in the same time Watson managed five.
He was particularly strong on the leg-side and retired after the 102-minute masterclass.
Marsh’s maiden century for Australia was against an impotent attack on a lifeless pitch, but nonetheless adds further intrigue to the selection debate.
“The boys couldn’t stop commenting on how hard he was hitting the ball,” Harris said.
“There’s two all-rounders that are pushing for spots and we saw them both bat beautifully.”