The increasingly intricate electromagnetic environment necessitates higher anti-electromagnetic interference capabilities for electronic devices, thereby demanding a flexible absorbing material that can adapt to multiple forms, is lightweight, and exhibits excellent electromagnetic wave (EMW) absorption properties. In this study, we have developed a novel flexible absorbing material (FAM) based on glass-coated amorphous magnetic fibers (SFs) and Dallenbach-like absorbing structures through wet forming technology. By combining high-performance absorbing fiber with textile structures, the FAM demonstrates EMW absorption performance along with lightweight flexibility and shape adaptability. This paper explores the influence of process parameters in wet forming technology on FAM formation; as well as examines the construction of broadband absorbers through structural optimization. A single-layer FAM with a thickness of 1.7 mm (SFs length 8 mm, content 3 g/m2) achieves an impressive reflection loss (RL) value of −60.1 dB at 11.6 GHz. Furthermore, optimized multi-layer FAM attains effective absorption bandwidth (EAB: RL ≤ −5 dB) across a wide range from 3–14 GHz. This work presents a new approach for developing ’lightweight, thin, wide, and strong’ absorbing materials based on fiber and textile structures which holds significant implications for civilian electromagnetic interference protection as well as military electromagnetic stealth technology.