open the hood and see if the P/S fluid is full and look at the serp belt. I would next check the transmission fluid and make sure it is full. Let me know if the sound changes with RPM changes or turning the steering wheel and if driving down the road or just in park idling.
let me know what you find
If the whining noise is from the transmission I do not think a flush will solve the issue.
what does the trans fluid look like, color?