I have tried adding the option -depth 12 to the string
convert transparentPNG.png -resize 500x400 -background white -flatten -depth 12 png_small.jpg
The input file is a transparent png to which I'm adding a background and then changing the depth. But the depth remains the same as 8bits. I verified the same using the -verbose.
I'm not sure what could I be doing wrong here. I'm referring to the site link
The transparent input png file used for my test can be found here
Let me know if you have any questions on the tests i did. Hoping to get some tips.
A JPG can only be 8-bit, so your internal 12-bit image is converted back to 8-bit when you save the result.