Pyelonephritis or Urinary Tract Infection (UTI): The presence of leukocytes (25 WBCs/mcL), high specific gravity of urine (1.035), protein in urine (30 mg/dL), and the patient's symptoms of right-sided abdominal and flank pain suggest an infection of the urinary tract, with pyelonephritis being a strong consideration given the location of the pain.

Nephrolithiasis (Kidney Stones): The patient's flank pain could be indicative of a kidney stone, especially if the stone is obstructing the flow of urine, which could lead to infection or inflammation, explaining the leukocytes and protein in the urine.
Acute Cystitis: Although the pain is more flank-like, which might suggest upper urinary tract involvement, acute cystitis (infection of the bladder) could still be a consideration, especially if the infection is severe or if there's an anatomical issue that refers pain to the flank area.

Appendicitis: Although the pain is on the right side, which is consistent with appendicitis, the urinary findings might distract from this diagnosis. However, appendicitis can sometimes present with urinary symptoms if the appendix is located near the urinary tract and causes irritation.
Sepsis from a Urinary Source: If the urinary tract infection is severe and has entered the bloodstream, it could lead to sepsis, a life-threatening condition that requires immediate attention.

Renal Infarction: This is a rare condition where the blood supply to the kidney is interrupted, leading to tissue death. It could present with severe flank pain and might have some overlap with the urinary findings if there's associated infection or inflammation.
Tubulointerstitial Nephritis: An inflammation of the spaces between the renal tubules, which could be caused by infection, drugs, or other diseases. It might present with similar symptoms and urinary findings, though it's less common than other diagnoses listed here.