Place an oven rack in the lower third of the oven; preheat the oven to 375 degrees.
Sift the flour and salt in a bowl. With an electric mixer on medium speed, beat the egg whites and cream of tartar until soft peaks form. Beat in the granulated sugar, 2 tablespoons at a time, until stiff peaks form. Beat in the coconut extract.
Sift one third of the flour mixture over the egg-white mixture and, with a large rubber spatula, gently fold in just until blended. Repeat with the remaining flour mixture, one third at a time, being careful not to overmix the batter.
Scrape the batter into an angel food cake pan; spread evenly. Immediately place in the oven and bake until the cake springs back when touched lightly, 35-40 minutes. Invert the pan on the neck of a funnel or bottle and let cool completely. To loosen, run a thin-bladed knife around the sides of the pan and around the center tube. Unmold the cake on a serving plate. If making ahead, wrap and let stand at room temperature overnight.
To make the glaze: whisk the confectioners sugar, pineapple juice and rum extract in a bowl until smooth. Drizzle evenly over the top of the cake and sprinkle with the shredded coconut.