Preheat air fryer to 375 degrees. Crumple a sheet of parchment paper, roughly 18 inches long into a ball, then unroll it and place into a 6-inch springform pan. Set aside.
Beat cream cheese, granulated sugar and brown sugar in a stand mixer fitted with a paddle attachment on low speed until the sugar has dissolved and the mixture is smooth, about 1 minute, scraping down sides as needed. Add the eggs, one at a time, beating on low speed until just incorporated before adding the next. Scrape down sides and bottom of bowl, Add whipping cream, lemon juice, salt and vanilla nd continue to beat on low speed until just combined, about 15-20 seconds. Sprinkle the flour over this mixture, and beat on low for 20 seconds more.
Place a mesh strainer over a large bowl. Pour the cream cheese mixture over the strainer in batches pressing with a rubber spatula until done, then pour the strained mixture into the prepared cake pan.
Remove the basket from the air fryer. Using tongs, carefully lower the cheesecake into the basket. Return the basket to the air fryer and cook at 375 degrees for 28 minutes. Remove the basket from the air fryer to check to see if center is still jiggly or the edges appear wet. If so, continue cook for 4-6 minutes. I cooked mine for an additional 6. The cheesecake is done when the top is very dark brown and the whole cheesecake moves together when jiggled. The top should only slightly slide around.
Remove the pan from the air fryer basket and transfer to a wire rack. Let cool on rack for one hour. Transfer to fridge and chill for 4 hours and up to 12 hours. Loosen sides of the pan and slide cheesecake from the pan. Gently remove the parchment. Serve.