Combine teriyaki sauce with 2 tablespoons pineapple juice from the canned pineapple. Reserve half of the pineapple teriyaki sauce for serving. Cook turkey burgers on a grill over medium-high heat until just cooked through. During the last minute of cooking, baste each side of turkey burgers continuously with half of the pineapple teriyaki sauce.
Grill pineapple until heated through and grill marks appear.
Combine mashed avocado with a generous squeeze of lime juice and Kosher salt.
Top each Flatout Foldit with turkey burger, turkey bacon, 2 slices of grilled pineapple, mashed avocado, and lettuce. Use reserved pineapple teriyaki sauce for serving, as desired.