How long does it take to heal leaky gut syndrome?

Leaky Gut. Difficult to say. Therapies vary and you likely need to try a few or even combine a few to get good control of the disease. And because it is an autoimmune disease, it tends not to go away but can go into a remission state with therapy.
Long time. There is no standard answer but in general months - years. This is a complicated process stemming from multiple possible sources. The gut is a slow organ to be damaged and to heal.