Reference: http://mufti.af.org.sa/ar/content/صلاة-الشكر
Question: He is asking about the prayer of thankfulness (salaah ash-shukr); about its time and how to perform it?
Response: Thankfulness [to Allaah] has no prayer. [Rather], that which is [authentically] established from the Messenger of Allaah (sal-Allaahu ‘alayhi wa sallam) is that when something pleased him, he would fall down in prostration to Allaah.