During D-Day, the Allies painted zebra stripes on all their aircraft to identify them as friendlies. Are there any records of the Luftwaffe painting zebra stripes on their own planes, to trick the Allies?

There are two things going on here with why the Luftwaffe did not use invasion stripes as a false flag.

One, despite the ubiquity of invasion stripes in plastic models and warbirds, they were not all that common for aircraft during the war. The most famous invasions stripes, the three white bands and two black ones used during Operation Overlord, were applied only at the start of the invasion and were for aircraft operating in the Normandy theaters. While there were plenty of aircraft carrying these stripes, they were only visible once the invasion began. Allied units began removing these stripes or painting them over once it became clear that the invasion was successful. This was a chaotic process as some units carried the markings through the summer of 1944 while other aircraft kept portions of the stripes such as underwing ones. Generally, most top wing stripes disappeared by July 1944 and underwing ones by September. Nor was the painting of the stripes uniform; field-applied stripes could be quite crude as seen in this photo and this C-47 pic while new planes delivered had more professionally-painted ones. This led to the stripes weathering over the course of operations, with some planes having pristine stripes and others less so like in this famous picture of a B-26. Thus invasion stripes were not as homogeneous for Germans to discern and hard to emulate.

The other reason the Luftwaffe did not use them is, simply put, the German air force was a hollow shell of itself by June 1944. One grim German joke captured this situation:

How do you identify whose plane that is? If it is green, it is British, if it is silver, American. If it cannot be seen at all, it is German.

The response of the Luftwaffe to Overlord bears some of this joke out. Luftflotte 3, the part of the Luftwaffe charged with defending northern France, managed to get over 300 sorties on 6 June. This might look impressive, but very few of these aircraft managed to reach the beaches, and that 300 number pales before the number of Allied sorties on 6 June which was in the 12000 range. Allied planners had actually anticipated a more robust response by the Luftwaffe to the invasion and this underscores the anemic nature of the Luftwaffe's response. Luftflotte 3 tried to up its attacks on the beacheads in the following days, but they kept running into a wall of Allied airpower.

Luftwaffe veterans' accounts from this time speak of even getting into the air as being a Sisyphean task as Allied air attacks on both airfields and the transport system made it difficult to get replacement planes, spares, and fuel. Applying invasion stripes to Luftflotte 3's planes might have made their jobs easier, but there were precious few planes available to the Germans to do so. Moreover, applying such conspicuous markings to their planes would have flew against the survival instincts of any German pilot in the summer of 1944 as they knew they were incredibly outnumbered and being visible was the last thing they wanted.