Why does flash make a brass subject look grey?

Well, no EXIF data to go by. The second looks like using a "Sepia" color filter. That would be my first guess, particularly given what happens to color in the rest of the image.

A second guess is that brass is actually highly reflective in the UV and near-UV parts of the color spectrum where the human eye is considerably less sensitive than camera sensors. If we are talking about a typical white LED as illumination, it has kind of a hole in the spectrum between the narrow-band blue color of the actual light-emitting semiconductor and the spread fluorescence spectrum making for the red-yellow-green part of the light emittance. That would make it prone to be less than properly yellow in digital camera pictures under LED lighting or UV-leaning lighting like that of the sun or an actual flash tube without UV filter.

Then there is the problem that a whole lot of lighting is not coming from the flash (check out the highlighted reflections on the round parts: only the reflection pointing straight to the photographer is due to the flash). That means that there is significant light input apart from the flash, and if the white balance is set to "the mobile's version of flash" as white balance setting, the external light source may mess it up. And non-photographic "white" LED lights tend to mix a pulsed narrow-band bluish light source with a semi-continuous yellowish fluorescence. Depending on just what phase you happen to capture, this can also lead to surprising colorings.

But all that fancy hand-waving aside: Sepia filter really looks like what, for whatever reason, happened here. Check the EXIF data of the original photograph.

The first shot is by ambient light. Likely this is warm shop florescent with maybe a mix of standard tungsten bulbs. It is this warm lighting that enhances brass. The second shot is flash. Modern flash outputs a colder light. Actually it simulates north blue sky lighting. You can try setting different color temperature or you could use a image editing software. Another approach is to buy a few inexpensive pin-up lamps with tungsten bulbs. Another approach is a warming filter. These are salmon colored glass or gelation filters that mount or tape over the lens. You want any one of the several color conversion filters. These are amber 85 -- 85B -- 85C buy then off the web.

My assumption is that the auto white balance took over.

The image, because you took the photo pretty close is dark everywhere except the brass. If the auto white balance is turned on, the warm tint of it was turned into a neutral color, gray.

See if it is the case. Take a test photo with white paper below. The camera will notice this white and use it to balance the white, leaving the brass alone.

This looks like a processor issue. It looks to me like the camera has chosen to use the sepia filter despite the fact that effects are turned off. A white balance error would skew the colors universally. not specifically toward sepia. What camera are you using? It may be time for a replacement.

LED flash is not white colour (continous spectrum like sun or edison or tungsten bulb). LED is RGB, a mixture of red, green, blue light. Cheaper / older (pseudo-)white LEDs accomplish this by using three separate LEDs (R + G + B). And as others have noticed there is a severe magenta cast in the flash picture which means there is no green in the picture. Could it be that your flash LED is broken / malfunctioning?