Scotland openers George Munsey (41 not out) and Michael Jones (45 not out) batted superbly to take the non-Test nation to 90-0 in a rain-interrupted innings of 10 overs after their skipper, Richie Berrington, won the toss at the Kensington Oval.
Because Scotland's innings was halted, for nearly two hours, on 51-0 off 6.2 overs, it meant England were left with a revised target of 109 in 10 overs under the Duckworth-Lewis-Stern method.
But before England could begin their reply, on a ground where they won the 2010 T20 World Cup final, a fresh downpour led the umpires to abandon the match, with both teams receiving a point each.
It was a frustrating end to Scotland's first T20 match against England and left them unable to press for a win that would have rivalled their shock 2018 six-run one-day international victory over their border rivals in Edinburgh.
Earlier, left-hander Munsey, on 16, top top-edged a hook off Mark Wood high to England captain and wicketkeeper Jos Buttler, only to be reprieved by the fast bowler's no-ball.
Chris Jordan was hit for 14 runs in three balls by Lancashire-born Jones, who had arrived at the tournament fresh from a stint with English county Durham. Jones's huge pulled six, which damaged a solar panel on the roof of a stand, was followed by two scorching fours.
When play resumed, revised restrictions limiting bowlers to a maximum of two overs each meant both Wood and fellow quick Jofra Archer had bowled out.
More boundaries followed as Jones and Munsey both smashed leg-spinner Adil Rashid (0-26) for huge sixes.