Neither are correct. How long do you estimate to finish it? Correct -->> How long do you estimate it will take you to finish it. <-- you don't have to put the "it" here. (as long as the person you are talking to knows what you are specifically talking about) You could just say "How long do you estimate finishing"

I respectfully disagree with Jerry. Both are correct and natural for spoken American/Canadian English. The first version is understood as a shortened version of the more formal second version.