Bronchiectasis is characterized by chronic infection and persistent inflammation of the bronchial walls, leading to continuous immune activation. This prolonged inflammatory state can trigger amyloid protein deposition in tissues, resulting in secondary (AA) amyloidosis. Amyloidosis is a known systemic complication because the ongoing inflammation increases serum amyloid A protein production, which aggregates and deposits in organs like kidneys. Other options such as diabetes mellitus, hypertension, and peptic ulcers are not directly linked as complications of bronchiectasis.

Reference: Harrison's Principles of Internal Medicine, J. Larry Jameson, 20th Edition.