Left-sided player O’Flaherty previously played for Rebels in the 2008-09 season and signed for the club after playing in the friendly with Brighton last Wednesday.
Defender Kessack had been with Rebels throughout pre-season and has also joined the ranks and Worthing boss Chris White said: “Chris has great quality and has played in the Premier Division and we know what he will bring.
“And Owen has done well for us in pre-season.”
Full-back Matt Piper (groin) and striker Scott Tipper (calf) are both struggling to be fit for the start of the league season on August 18 and White does not expect midfielder Tom Manton (ankle) to be back until October.
Midfielder Scott Kirkwood is also out for the first three matches of the season after picking up 15 yellow cards last season.
Rebels head to local rivals Bognor Regis for a friendly on Friday evening (7.45pm), with White hoping defender Glen Woodburn (calf) and Alan Mansfield (back) will be back after they both missed the 3-0 defeat to Whitehawk on Saturday.
White said: “We played well for an hour against Whitehawk and matched them but they are a very good side and I think they’ll do well again this year.
“We had seven players missing and they had a few missing as well but they’ve got plenty of strength in depth.”
Rebels will have keeper JJ Banasco-Zaragoza in their squad for the game at Bognor and midfielder Paul Kennett is also back available.