In my experience, they way you accomplish this is by adding either a formula or button field to your Airtable, with the formula
"https://forms.fillout.com/yourformurl" & RECORD_ID()
Fillout should provide you the appropriate url link. That will compile the direct link to a fillout form for each individual record that whoever can update. Then it's about sharing that link with people. The simplest way is to email (individually on a small scale, automate for larger scale).
Keep in mind too that the Update Record Fillout Form and the Create Record Fillout Form are two different types of connection, and if you want people to submit a new record via Fillout and then be able to edit that record, it requires both types of form.