C H Gardener suggests that Fleming mentioned the possibility of using two valves in opposition to generate oscillations. What is missing is any citation of a source, and two thermionic diodes do not generate oscillations. They can make a full wave rectifier, as Fleming illustrated, or back to back will clamp a signal.
Fleming, in his patents and his intention, claims his diode as a means of detecting RF signals and over the decades the diode as signal detector was most successful.
It has not been possible to substantiate C H Gardener's suggestion but it is possible to present what Fleming did actually patent. Here is Fleming's paper from January 24, 1905. And here is his patent submitted April 10, 1905 and granted November 7, 1905.
Thanks to Stig Comstedt for pointing out this possibly misleading statement in the original article and for providing the two PDF files.