Lipoma: Given the description of the mass as soft, fatty, and non-tender, lipoma is a strong consideration. Lipomas are common, benign tumors composed of fat tissue that can occur almost anywhere in the body, including the abdominal and flank regions.

Renal Cyst: A simple renal cyst could present as a soft, non-tender mass in the flank. While renal cysts are usually detected incidentally on imaging, a large cyst could potentially be palpable.
Colonic Diverticulitis (Chronic): Although the patient does not have a history of trauma or flu-like symptoms, chronic diverticulitis could potentially cause a palpable mass in the left lower quadrant, especially if there is a significant amount of associated inflammation or a diverticular abscess that has become chronic and less symptomatic.
Splenic Cyst or Mass: A splenic cyst or a mass such as a splenic lymphoma could present as a left upper quadrant or flank mass. However, splenic lesions are less likely to be described as soft and fatty.

Retroperitoneal Sarcoma: Although rare, sarcomas can present as large, soft tissue masses in the retroperitoneum. They are critical to diagnose early due to their potential for malignancy and the need for prompt treatment.
Pheochromocytoma: A pheochromocytoma, a catecholamine-secreting tumor of the adrenal gland, could present as a mass in the flank. While it might not typically be described as soft and fatty, missing this diagnosis could be catastrophic due to the potential for severe hypertension and other systemic effects.
Abdominal Aortic Aneurysm (AAA): Although the mass is described as non-pulsatile, an AAA could potentially present without a palpable pulse, especially if it is thrombosed or if the patient is obese. AAA is a critical diagnosis to consider due to its high mortality rate if ruptured.

Retroperitoneal Lymphoma: Lymphoma involving the retroperitoneal lymph nodes could present as a mass in the flank or abdomen. It is less common but should be considered, especially in the context of systemic symptoms or other signs of lymphoma.
Neurofibroma or Schwannoma: These are benign nerve sheath tumors that could occur in the retroperitoneum and present as a soft tissue mass. They are less likely given the description but could be considered in the differential diagnosis.
Gastrointestinal Stromal Tumor (GIST): A GIST could present as a mass in the abdomen, although it is less likely to be described as soft and fatty. GISTs are rare tumors of the gastrointestinal tract that can occur anywhere along the GI tract.