European junior champion Dixon finished second in the men’s 10m preliminary round behind Great Britain team-mate Matty Lee.
Dixon was down on his best, scoring 392.15 points, but he will be hoping to hit top form in the final on Sunday.
Joining him in that final will be team-mate Heslop, who qualified fifth with 364.35 points on Friday.
However, there was frustration for fellow Plymouth youngster Alfie Brown, who missed out on reaching the final by less than three points. He finished ninth in the prelims, with only the top eight progressing.
Sinclair, who along with Heslop competed at last week’s FINA Grand Prix in Madrid, secured a place in Sunday’s women’s three-metre final.
Despite not hitting her best form in the prelims she still secured an all-important top eight place with 237.55 points.
Sinclair and Heslop had suffered disappointment on the opening day of the championships by missing out on the mixed three-metre synchro title by less than a point.
They scored 269.82 points but were just edged out for gold by Sheffield’s Millie Fowler and Ross Haslam, who scored 269.82 points.
There was also frustration for Dixon in the synchro events. He and his partner Noah Williams, from London, had to settle for second in the men’s 10m synchro final on Friday after dropping their fifth dive.
The duo had impressed earlier this year at the National Cup in Plymouth and looked on course to win in Edinburgh, but after their disappointing penultimate effort they were overtaken by home pair of James Heatly and Lucas Thomson.
Edinburgh divers Heatly and Thomson scored 362.34 points, with Dixon and Williams collecting 352.62.
Heslop, Shanice Lobb and Tonia Couch will all be in action on Saturday.