Clooney is asking the warden to ensure him that if he (Clooney) offers the information up, the warden will allow him (Clooney) special favors with regard to his work detail.

This film is adapted from an Elmore Leonard novel called "Out of Sight". The exact text is in the ref URL linking to a preview in the book.

"The Pup" is the warden, "Foley" is the character Clooney plays. When 'the Pup' says "you turn fink?" it means to 'rat out'. Foley explains his reasons for doing this. Foley says "I'd expect you to look out for me as long as you're here. Let me run my business, keep me off work details." He wants to have it easy inside the prison in exchange for the information.