The Rebels dominated the opening 45 minutes and could well have gone into the half time interval further ahead than the two goals they managed to score.
James Dobson was narrowly wide with another long-range rocket and Perry Coles was denied by a good save after good work from Flood.
The opening goal arrived on 12 minutes and was the result of nice link-up play between Coles and Flood, with the latter finding the top corner.
The lead was doubled just nine minutes later as Coles teed up Jackman to fire into the bottom corner.
Lee Togwell was denied by a save and Flood deftly flicked a Jackman cross just past the post as Slough threatened on numerous occasions.
Ben Harris and Manny Williams were introduced in place of Dobson and Coles at the break and Slough continued where they left off, creating further chances with Louie Soares firing over and both Flood and Williams having efforts saved.
Kingstonian pulled a goal back on 52 minutes with Louie Theophanus nipping in to score after a short backpass from Nathan Smart.
There were chances galore at both ends as the half wore on - Flood missed a great chance to restore his side's two-goal lead, whilst former Rebel Elliot Buchanan crashed a shot against the crossbar for Kingstonian.
The visitors had further chances and Scott Davies also saw a fantastic effort from a free kick saved by the Ks goalkeeper.
Jackman narrowly failed to register his second goal late on, but Slough made sure of the win with the last action of the game when Ben Harris headed a George Wells cross home from 10 yards.
Slough Town Line up
Jack Turner, Josh Jackman, George Wells, Sam Togwell, Nathan Smart, Lee Togwell, James Dobson, Scott Davies, Perry Coles, Chris Flood, Louie Soares. Substitutes (all used): Sean Fraser, Mark Nisbet, Ben Harris, Manny Williams.