Business Analyst positions vary inside Amazon depending on the team. If you are applying for a more technical function, you should expect some technical questions. It will not be as complex as Software Development Engineer (SDE) questions, but you should expect some technical questions relevant to you job.
A business analyst is likely to be asked to run queries against the data warehouse, so you should expect a healthy amount of SQL questions. You need to be good at SQL to pull reports out of data warehouse/BI systems.
A business analyst is an execution focused individual contributor position. You should demonstrate your agility and bias for action, ability to get things done, and not afraid of diving into details.
You should read Amazon Leadership Principles, and prepare specific examples. I get into many details in my book How to Get a Job at Amazon. Follow the framework and you will be on the right track.
Apply the STAR (Situation, Task, Action, and Result) technique when answering Amazon Leadership Principles questions. You should prepare for at least one example for each of the Amazon Leadership Principles. Ideally, your example should come from your recent work experience. If you are a recent graduate, use examples from internship/co-op. If you run out of work examples, then you can use examples from school, volunteering activities or even personal situation. Use the STAR technique to describe each example methodically. Please be concise and to-the-point.