In a medium skillet, drizzle a little olive oil and smear with a towel to coat the pan over medium heat.
Pour in 2 of the egg whites and cook until set and golden, about 1 minute. Flip and cook on the other side until golden. Remove from pan and repeat with remaining egg whites, 2 at a time.
Once the egg whites are finished and set aside, add tomatoes and spinach to pan. Cook until spinach begins to wilt, about 1 minute.
Stir in feta cheese until heated through. Remove from heat.
On each tortilla, fold the cooked egg white and place in middle, then top with 1/4 of the spinach mixture. Fold in the wrap and serve immediately.