Manager Jonathan Morgan elected to keep the same starting XI for the third time in a row after a league success over London Bees was followed by a penalty shootout win at Birmingham City in the Continental Tyres League Cup.
Libby Smith and Charlie Devlin - in action against her former club - also went for goal from distance, before Flint forced a save from Cumings on the half-volley. Charlton, though, were standing tall.
As a light drizzle descended, Leicester continued to press and, on the half-hour mark, Devlin was unlucky to see her low drive saved after bursting through Charlton's rearguard to get a shot off.
She was there again just moments later to force another impressive stop from Cumings after weaving her way into a pocket of space and looking to find the top corner. Her curling effort, though, was well stopped.
The scales tilted in City's favour on 33 minutes, meanwhile, as former Leicester midfielder Ella Rutherford earned herself two bookings inside 60 seconds to leave her side with a numerical disadvantage.
The Foxes almost punished Charlton straight away, too, when Devlin's free-kick came through to Sam Tierney on the left and, while Remi Allen got her head on it, Cumings was there to frustrate the visitors again.
There was little the hosts' shot-stopper could do about the opener, though, as Flint arrowed an absolute rocket into the bottom corner from the edge of Charlton's box - a fitting reward for Leicester's efforts.
After the break, the Addicks posed more of a threat in the early stages and could have levelled the scores when Charley Clifford got her head to Bethan Roe's corner, but Kirstie Levell stopped it well.
Lachante Paul, though, was unfortunate not to double the visitors' lead on 67 minutes as Bailey-Gayle's cross eventually came through Charlton's box, but her attempt was too high to trouble the 'keeper.
City needed a second to be sure of their fourth straight win in the league and it came, finally, with 12 minutes to play, courtesy of some excellent wing play from Devlin, who danced past two defenders to cross.
The ball in was perfect too, landing on the head of Allen, who couldn't miss from less than six yards out to calm any nerves which may have existed for the travelling Foxes.
Second-half substitute Liv Fergusson went close at the very end, too, but the job was already complete for in-form Leicester.
City doubled their lead through Remi Allen in the latter moments in Dartford.
City were ahead and looking good, but a disconcerting threat remained. Charlton were looking dangerous on the counter, despite being a player down.
However, as the clock struck 78 minutes, a moment of magic from Charlie Devlin and a composed header from Remi Allen wrapped up all three points for Leicester.
Natasha Flint's opener was as stunning as it was important for the Foxes.
Natasha Flint's first season at the Club just gets better and better. Signed from Blackburn Rovers in the summer, the former Manchester City forward added her 10th goal in Leicester's colours on Sunday.
The quality of her 38th-minute strike, too, was brilliant - a fearsome drive from distance - but that will come as little surprise to anyone who has followed her maiden campaign with the Foxes.
Where does it leave us?
Charlie Devlin was playing against her former club on Sunday.
City remain top of the FA Women's Championship - on 23 points - for a second successive weekend following their seventh victory in 10 league outings.
Durham, who secured an admirable comeback win at Coventry City, continue to trail LCFC Women by just a solitary point. Third-place Liverpool, meanwhile, are behind by two.
Sophie Barker skippered the Foxes at Charlton.
The Foxes' final competitive fixture of 2020 takes them to the Sir Tom Finney Stadium to face Blackburn Rovers on Sunday 20 December (2pm GMT kick-off).
City: Levell; Smith (Howard 62'), Tierney, Plumptre, De Graaf (Cataldo 84'); Allen, Barker (c), Devlin (Blanchard 84'); Bailey-Gayle, Flint (Farrow 68'), Paul (Fergusson 84').
Subs not used: Riglar, Everett, Camwell, Thomas.
Goals: Flint 38', Allen 78'
Images: Charlton Athletic
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