I think Mr Shepherd was starting rumours. We are told that his "interest was involved in the reality of Sir Walter's retrenching" so he had motive. Even though Sir Walter banned the word advertise, I think Mr Shepherd would have started spreading the word that Kellynch was to let.

I don't know if Admiral Croft heard about it second-hand, it is possible that Mr Shepherd approached him directly on hearing that the Admiral was looking for a place, as you suggest. The risk with that for Mr Shepherd would have been if Admiral Croft had mentioned that Sir Walter's lawyer had approached him first.