Explanation from BA is "…..I would like to inform you that the lounge at Frankfurt airport is a third party lounge and Silver Executive Club members do not have access to that lounge." Is this correct?
Yes, technically. Silvers are allowed into the lounge when their flight is on a Oneworld carrier regardless of the flight number. Flybe is a code share partner, but not an OW member. You could have gotten into a lounge for 25€, though:
http://www.frankfurt-airport.com/con...s/lounges.html
Note: The BA lounge is still on the English page, but has disappeared from the German page.