Just use do shell script:
do shell script "mkdir -p ~/Desktop/Test
cp /Users/*/Library/Logs/DiagnosticReports/* ~/Desktop/Test" with administrator privileges
Or loop through folders of (path to users folder)
:
tell application "Finder"
if exists folder "Test" of desktop then
set d to folder "Test" of desktop
else
set d to make new folder at desktop with properties {name:"Test"}
end if
repeat with f in (get folders of (path to users folder))
tell contents of f
if exists folder "DiagnosticReports" of folder "Logs" of folder "Library" then
duplicate items of folder "DiagnosticReports" of folder "Logs" of folder "Library" to d
end if
end tell
end repeat
end tell
If you don't have permissions to read the files of other users, you can run Finder as root with launchctl unload /System/Library/LaunchAgents/com.apple.Finder.plist; sudo /System/Library/CoreServices/Finder.app/Contents/MacOS/Finder
.