4 yr old has had chronic cough for 12wks+.Has been diagnosed & is treated for acid reflux & asthma. Also diagnose w/ lrg tonsils/adenoids. Cause 4cough?

All of those. Cough is a symptom of "something" and in a 4 year old, things such as acid reflux, asthma, nasal allergies, and chronic infection (chronic tonsillitis for example) can cause this. Treatments for each are different and often, these things can occur together. If the treatments for reflux, asthma, and allergies are not working, you should see an ENT to get an opinion about the tonsils and .Adenoids.
All of the above. Prolonged cough can be the result of asthma, nasal allergy and gerd. The large tonsils and adenoids may be normal for age, but are more likely the result of nasal allergies. If he continues to cough, his treatment may be insufficient or there is something in the house that triggers his symptoms. If he hasn't yet been evaluated by an allergist, he should be.