O'Flaherty finished behind English duo Gemma Steel and Jenny Spink in Dublin.
Defending women's champion Fionnuala McCormack was a late withdrawal from Sunday's race because of a hip niggle.
Mullingar's Mark Christie won the men's race in a respectable 29 minutes and 30 seconds, leaving him ahead of England's Graham Rush (29.41) and Irish Olympic athlete Mick Clohisey (29.44).
The event also doubled up as the Irish championship for the 10km road race distance so O'Flaherty and Christie lifted the national titles.
As the Irish men packed well with Sergiu Ciobanu fourth in 30:20 and Kevin Dooney (30:38) sixth, the home nation pipped England by 40 seconds in the team match, which was decided by the aggregate times of the four scorers in both races.
Ireland's combined time was three hours, 15 minutes and 29 seconds and the team element gave the event added excitement even after the first three had crossed the line in both races.
The team success earned the Irish the Sean Kyle Cup, competed for in memory of the highly respected Ballymena & Antrim coach, who died in November 2015.
Kyle formed a remarkable coaching partnership at the club with his wife, the three-time Olympian Maeve Kyle and event organiser Gareth Turnbull came up with the idea last year of marking the Ballymena & Antrim stalwart's contribution to the sport by staging the team event.
Newcastle athlete O'Flaherty stayed with former European Cross Country champion Steel and Spink for the opening 5km in the Phoenix Park before the English duo broke clear.
Steel crossed the line in 34:15 which left her nine seconds ahead of Spink, with Rio Olympics steeplechase competitor O'Flaherty a further 14 seconds back in third.
The women's top six was completed by three more Irish athletes as Claire McCarthy (34:47) was followed by Laura O'Shaughnessy [35:04] and City of Derry's Catherine Whoriskey (35:55).
McCormack was forced to withdraw because of injury on Sunday morning.
With a series of races, including junior events, taking place, over 8,000 runners were in action at the Phoenix Park.
County Down athlete Kerry O'Flaherty's third place at the Great Ireland Run helped Ireland clinch the team honours.