The typical microwave absorber usually exhibits the large variations in absorption behavior with absorbing thickness (>10% for a change in absorber thickness by 10%). How to obtain broad, strong and stable microwave absorption performances still remains a challenge. In this work, a vertical ball milling technique followed by a co-deposition method in alkaline solution is developed to prepare polydopamine (PDA)/polyethyleneimine (PEI) coated flaky FeSiAl composites, which display broad, strong and stable absorption performances at 2-14GHz. The obtained PDA/PEI covered FeSiAl flakes exhibited minimal reflection loss (RL) values exceeding -20 dB at 2.5-8.9mm. When the effective absorption bandwidth (EAB, 4.4-4.88GHz) and absorption efficiency (RE, 12.11-13.24dB·GHz/mm) change by 10%, the corresponding change in absorption thickness can be achieved 28.57% (2.5-3.5mm) for EAB and 15.63% (2.7-3.2mm) for RE. Phase cancellation and electromagnetic loss contribute to large and stable RL peak intensity and the large loss factor over a wide frequency range lead to broad and stable EAB. Integrated with a macroscale structural design, frustum of a cone structure established by computer simulation technology is beneficial for integrating quarter-wavelength resonance, dielectric loss and magnetic loss, resulting in wide EAB of 12GHz (covering from 2-14GHz) and strong RL of -62.27dB at 7.1GHz.