Eberhardt did not command only a three-plane Kette of his own but the whole flight/squadron/staffel of six Heinkel 51´s (two Kettes) flown by Germans (Sonderstab W) during the late summer/early autumn 1936. The first six Heinkels were coded "2-1" to "2-6" so the planes of Eberhardt Kette were coded between 2-1 to 2-6.
One should not blame the Nationalist Spanish pilots (Escuadrilla Rambaud) for the written offs of first Heinkel 51´s - two of them were indeed damaged in less happy landings but were repaired and later put in action by the Germans.
The first recorded Heinkel 51 loss was the "2-4" which was was shot down on 30.8.1936 by enemy Dewotine 372 (
Ramón Puparelli Francia being most likely the pilot who shot Trautloft down although his claim has been recorded on 2.9.1936 by Republicans). A second Heinkel 51 was lost on 28.9.1936 in flight accident when Ekkerhard Hefter crashed his plane to the townhall of Vitoria while displaying aerobatics at low level and he was killed - but I do not know what was the number of that plane. The third Heinkel loss - I guess - was the plane piloted by Eberhardt himself which was lost during the famous air battle over Madrid on 13.11.1936 but again I do not know the number of the plane.
When it comes to the three pilots of Eberhardt Kette, they were Eberhardt himself, Hannes Trautloft and Herwig Knüppel. So at least Knüppel´s name can be added to the list of pilots flying Heinkel 51´s of Eberhardt Kettel. Other fliers of the first German He 51 detachment were Wolf-Heinrich Houwald, Ekkehard Hefter and Alfons Klein.
Ten more German fighter pilots came to Spain by October with a new batch of Heinkels when the strength of German fighter detachment grew to 14 planes. Probably some of them flew also the planes of "the original Eberhardt Kette".
I would advice to look for more details from Hċkans Aviation Page (if you have not already checked it):
http://surfcity.kund.dalnet.se/scw.htm