In May 2021 I heard from April who had a Dell Wyse 3040. Her version was fitted with 16GB of flash. As part of her exploration of the thin client she had tried out Windows 10.
I can confirm that Windows 10 does run on this, although, with only 16GB of flash on board, you will need to install it on an external device. (I used an SSD paired with a USB adapter). There don't appear to be any working sound drivers for the 3040 in the standard Windows 10 installation.
It's very slow, but it does run.
In February 2022 she provided some clarification and an update:
As far as I can tell this model uses that bizarre I2S sound system. This requires board-specific drivers for Windows, and, as Dell does not support Windows on this model, said drivers seem not to exist. It's not that they don't exist in the standard Win10 installation but (as far as I can tell) they don't exist at all.
On a related driver issue: I've noticed that Windows 10 versions newer than 1803 refuse to install the video drivers for this model. This happens with both automatic and manual installation options. However, if I start by installing 1803 which DOES install the video driver and then perform an upgrade to the latest version, it works. It's just a shame this takes so long (several hours) to do on a processor this slow...
In October 2022 I heard from Mat who noted the comment below from Jin re drivers for Windows 8.1. and the HP Pro Tablet 608 G1. He tracked down this link to a CAB file with the Windows 10 sound drivers.
The link is to a windows update cab file, extract this to a folder and use device manager to load the sound driver
In May 2022 I heard from Jin.
As noted by April above Windows 10, whilst it can be installed on the 3040, in reality it is too slow to be useful. However this is not true of earlier versions and Jin installed Windows 8.1.
After installing it I found that many drivers were missing so I set out to look for PCs that had similar hardware and in particular used the same CPU. I eventually tracked down the HP Pro Tablet 608 G1. (The Atom X5 Z8500 in the HP tablet and Z8350 in the Wyse thin client are from the same CPU family). The HP tablet runs Windows 8.1.
Using the chipset driver from the HP support pages solved a lot of the problems.
The driver comes in their usual softpaq executable format which by default expands the files into the directory swsetup. Having expanded the files you should use Device Manager to search for the wanted drivers in this directory. Do not use the standard installer. If you do you will find that subsequently Windows will fail to start.
It is a similar exercise to get the sound to work. Unfortunately I can't remember where I found the driver for this. I only tested the speaker part, and that works fine.