Rinse mushrooms and place in a bowl with enough cold water to cover; soak until mushrooms are re-hydrated, about 15 minutes. Drain and slice mushrooms.
Combine 4 cups chicken broth, water, potatoes, carrots, barley, and black pepper in a pot; bring to a boil, reduce heat to low, cover the pot, and simmer until barley is cooked, about 1 hour.
Heat oil in a skillet over medium-high heat; saute onion and garlic in hot oil until golden, 3 to 5 minutes. Add onion and garlic to barley mixture, bring soup again to a simmer, cover the pot, and cook until flavors blend, about 30 minutes.
Whisk remaining chicken broth and flour together in a bowl until smooth; stir into soup, bring to a simmer, and cook, stirring occasionally, until soup thickens, about 15 minutes.