Try this command:
rsync -a -f"- */" -f"+ *" /home/user/ destination/
man rsync
-f, --filter=RULE add a file-filtering RULE
The rule to include all files* and exclude the dirs */
Another approach to use the regular copy cp
cp /home/usr/* /destination
you can get rid of the errors about dirs using redirection
cp /home/usr/* /destination 2>/dev/null
This will only copies the files inside your home without the directories
If you want to exclude all *.sh from all subdirectories:
-f”- */*.sh”