Goalkeeper Flinders and midfielder Berrett joined from Hartlepool and Yeovil respectively on Tuesday and Wilcox wants to further strengthen.
“We hope to add a couple more if possible,” Wilcox told the club’s official website.
“The backing from the chairman and board has been first class and everything I have asked for I’ve managed to get.
“I’m very positive and can’t wait to get going now.”
Wilcox, who signed striker Vadaine Oliver from Crewe last month, replaced Nigel Worthington in October and is preparing for his first full season in charge at Bootham Crescent.
He added: “We are trying to recruit in the right way by not only bringing in players with experience, but who have also performed at a higher level.
“I’m pleased with the additions we have made to the squad right the way through the spine.
“We’ve added competition for places which is always important, as well as possible game changers from the bench which you look at as a manager.”