It’s important to clarify that in a clinical setting, dandruff is associated with seborrheic dermatitis, which is not (and is not treated) the same as psoriasis. From UpToDate:
Seborrheic dermatitis in adolescents and adults. Denis Sasseville MD, 2018.
Scalp — The mildest and most common form of scalp ...
There is no blood test that can definitively diagnose psoriasis
The article linked from the question (Arthritis.org) mentions several studies; in one of them uric acid was elevated in only 20 percent of patients with psoriasis. In another study, it was psoriatic arthritis that was most strongly associated with elevated uric acid. So, it may ...