The 46-year-old Flower has quickly immersed himself in the club's social scene too.
"He joins in, he doesn't disappear quickly after sessions," Stratford chairman Steve Cootes told the BBC. "He's one of the lads.
"He has a beer afterwards. He's open and engaging, talking about his time in cricket. It's fascinating and inspirational for us to listen to him."
Cootes said former Zimbabwe test batsman Flower had turned down his offer to play for the club but indicated that he may stay on as coach on a long-term basis.
"He's very hands-on," added Cootes. "He takes one-on-one coaching sessions. On the first night he turned up, only a few of us were aware...a number of people looked up in disbelief."
Flower resigned as team director in January after England's embarrassing 5-0 Ashes defeat in Australia.
He is still employed by England as a technical director of elite coaching.
(Writing by Tim Collings, editing by Tony Jimenez)
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