One good way to potentially if your ancestor had War of 1812 military service in the US is to search and see if a warrant was issued in his name at the Bureau of Land Management (BLM) website.
Many of the men who were veterans of that war and were living in the 1850s qualified for land that was made available to them at that time. These veterans were given a warrant for a stated number of acres, which could be exchanged for a patent that would give title to a specific piece of federal land. Many veterans never actually claimed any land, instead they sold their warrant to someone who actually wanted to settle.
So your ancestor who never left Kentucky may have a warrant for land based on his War of 1812 service for property that was patented (actually located) in Iowa. The same holds for a veteran from New York State.
When searching the warrants at the BLM site, don't restrict the state. Are you CERTAIN your ancestor's warrant wasn't used to obtain property elsewhere?