Place chicken in a large pot. Pour white wine and chicken broth over chicken; bring to a boil. Cook chicken until no longer pink in the center, about 45 minutes. Transfer chicken to a work surface using a slotted spoon. Shred chicken.
Mix chicken, yogurt, and mayonnaise together in a bowl. Add scallions, mustard, tarragon, sea salt, onion powder, kelp, and white pepper; mix well. Cover bowl with plastic wrap and refrigerate, 1 hour to overnight.