Can the flu cause elevated psa levels?

Not really . It may increase the psa very slightly but only briefly as part of an inflammatory response. But, generally, no. The psa should not be elevated high enough to worry. If it is, you need it checked out.
Not typically. Urinay tract infection, urinary retention, prostate inflammation or infection, benign prostatic growth, and recent ejaculation have been shown to cause transient benign increases in psa values. The half life of the psa molecule in the blood stream is long enough that repeat checks should not occur any closer than 4 to 6 weeks apart to represent a new value.