I had tried to make batch script that copies all *.tif files located in D:\\images(random named subfolders here) to d:\\all.
xcopy D:\\Downloads\\*.TIF D:\\temp\
FOR is your friend. Read HELP FOR on the /R option and the %~nx variable substitution; and then try this very simple code.
pushd d:\downloads
for /r %%a in (*.tif) do (
echo COPY "%%a" "d:\temp\%%~nxa"
)
popd
watch carefully the results and then remove the ECHO command.
You will have to refine the code to cope with errors, duplicate names, edge cases, names with reserved characters, race conditions, cosmic events...