If it doesn’t let people add new linked records that don’t already exist, then you can use an automation tool like Integromat to act as the middleman between JotForm and Airtable. Just be sure to turn on “Smart Links” in Integromat to allow the entry of new linked records.
Then, as I mentioned above, you could use an automation platform such as my favorite Integromat to act as the middleman between JotForm and Airtable. However, it could get pretty tricky to parse the text arrays that JotForm sends to Integromat, so it can get complex pretty quickly.
An easier route that I also mentioned above would be to use MiniExtensions.com as your form software.