The duo came to the crease with the home side on 108-5, and then proceeded to put on 204 runs for the sixth wicket, Walmsley smacking 102 not out from 119 balls, including 14 fours and two sixes, while number seven bat Hatton smashed six sixes and 14 fours in his explosive unbeaten 116 off just 92 deliveries.
Folkton & Flixton posted 312-5 from their 50 overs, Ollie Thane the top Welton bowler with 3-69.
Jadon Wilson was the pick of the home bowlers with 3-33 as Welton never looked like surpassing Flixton's total, Elliot Hatton capping a superb all-round day with 2-56, Charlie Colley chipping in with 2-34 the visitors were pegged back to 190-9.
Scarborough Athletic's home National League North campaign off to a winning start against Hereford
Breidyn Schaper sparkles with the bat as Scarborough CC experience mixed weekend
Folkton & Flixton CC net fifth YPLN Championship win in a row on the road at Easingwold
PHOTO FOCUS - 17 photos from Scarborough CC v Sessay CC by Simon Dobson
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Welton skipper Chris Lound scored 51 not out and Ben Wilkinson 40 to offer some resistance.
Sixth-placed Folkton & Flixton's next league match is at home to third-from-bottom Whitkirk on Saturday.