WATCH: Trump Spox Accuses Obama Of Promising A "Vaccine" And Failing
COVID-19 did not exist when President Obama was in office, so Obama could not have created a vaccine for it. Absent time travel, Kayleigh's claim is logically impossible.
Assuming Kayleigh is talking about H1N1: Under President Obama, a vaccine was developed for H1N1. President Obama was vaccinated with it. (see video at link)
In an interview today with American Urban Radio Networks in the Oval Office, the President made clear that the time for adults to get their H1N1 shots is now and that it is safe. See the photo of the President getting his shot.