Their 367-run partnership in a 425-1 total - the second highest in List A games - saw the Lions beat Sri Lanka A.
Duckett's 131-ball 220 not out was the ninth-highest List A score ever, while Bell-Drummond hit 171 off 139.
"Those guys are very capable of playing international cricket," said Flower, who now coaches the Lions.
It was a successful tri-series for Flower's team, as the Lions beat Pakistan A and Sri Lanka A twice apiece, with batsmen scoring more than 150 in each fixture.
Duckett scored 163 not out in a seven-wicket victory against Pakistan A on 19 July, before excelling again in Monday's 140-run win.
Dawid Malan - the 28-year-old Middlesex batsman who received his first England call-up for the Twenty20 squad against Sri Lanka in June - struck 185 in an 88-run Duckworth-Lewis win against Sri Lanka on 21 July.
Full international Sam Billings, who has played five ODIs and seven T20s, hit 175 in Sunday's second victory against Pakistan.
"I think English cricket will be better for these guys having to force their way in," Flower, who led the national team from 2009 to 2014, told the Tuffers and Vaughan Cricket Show on BBC Radio 5 live.
"These youngsters have to push their way in and earn their spot. It was an incredible series of innings and great partnerships, the selectors will almost certainly take interest in these results."
And the 48-year-old had special praise for Northants' 21-year-old opener Duckett, who he described as "a very talented young man".
"None of us can foresee the future but there's no reason why he can't go on and have a very successful international future," he said.
England Lions batsmen Ben Duckett and Daniel Bell-Drummond could play for England within a year, according to former national coach Andy Flower.