Heslerton posted 144-8 batting first, Rob Middlewood hitting 58 as Harry Walmsley took 4-17 and Rich Malthouse, Jake Hatton, Jamie Nesfield and Connor Stephenson took a wicket apiece.
Flixton cruised to their victory target in reply as Malthouse hammered an unbeaten 89 and his opening partner Jake Hatton added a composed 39 not out as the hosts and holders finished on 146-0 in 23.3 overs.
Will Norman’s men will take on Ebberston in the third round of the North Yorkshire North group on Sunday May 26, with the winner of that encounter taking on either Cayton or Sheriff Hutton Bridge in the regional final on Sunday June 9.
Ebberston had a bye in the first round and were then handed their second round tie by Silton.
Cayton made it through to the third round courtesy of a victory against Sessay in the first round and a walkover against Staithes in the second round.
Sheriff Hutton Bridge beat Forge Valley by seven wickets to set up their third round clash with Cayton.
In the North Yorkshire South group, Staxton conceded their first round encounter against Addingham.
The final of the 2019 Cricketer National Village Cup, again to be held at Lord’s, is pencilled in for Sunday September 15.