Add white wine and reduce heat to medium-low. Simmer until wine is reduced by half, about 5 minutes. Add chicken broth.
Whisk flour into milk until all lumps are gone. Slowly whisk into sauce mixture. Increase heat to medium and stir until sauce reaches desired consistency.
Add chicken, bacon, green onions and oregano and stir until heated through. Season to taste with salt and pepper.
Pour sauce over cooked linguine and serve immediately.