The state of Kentucky didn't start recording deaths until 1911. Some counties of Kentucky have death registers starting in the early 1850's but the law wasn't enforced and they are not complete. For a death as early as 1824 you'll need to look for probate records or other types of records filed when someone died. I doubt there would be obituaries then for most areas of Kentucky. If he was a soldier in the Revolutionary War or the War of 1812 you might find pension records that would be of help.