Preheat oven to 425 degrees. Place folded pastry on a lightly floured work surface; roll out to a 12-by-14-inch rectangle. Trim edges to make even.
Place pastry on a parchment-lined baking sheet. With a sharp paring knife, lightly score dough to form a 1-inch border. Using a fork, prick dough inside the border every 1/2 inch. Sprinkle the border with 2 teaspoons sugar. Refrigerate until slightly firm, about 10 minutes (or up to 1 day, covered with plastic wrap).
Bake chilled dough until puffed and golden brown, 10 to 15 minutes. Meanwhile, in a large bowl, gently toss sliced nectarines with 1 tablespoon flour, remaining 1/3 cup sugar, and salt.
With a fork, press dough inside border to make level; arrange nectarines in rows on top (or pile nectarines on top and then spread evenly).
Bake, loosely tented with foil, until nectarines have softened, about 10 minutes.
Brush nectarines with warm jelly. Let cool to room temperature, about 20 minutes. To serve, cut into eight pieces.