The most important questions you should be asking are related to how many flatheads have they recently built and do they have the necessary experience, tooling and skills to do the work? The area where many screw up is in the valve train - there are specific valve-guide pilots that are unique to flatheads, there is knowledge related to valve angles and value heights, machining procedures, etc.. All engines are NOT the same.
Procedures & Parts - Cost Estimates: There can be quite a bit of labor involved in building one of these engines correctly - so it is very important to get a quote for what they plan to do, the costs, the parts they're going to use, etc.. If you don't do this, you may be surprised on what the actual budget needs to be.
Assembly and Warranty: If they assemble it - does it include a warranty . . . if you assemble it . . . I'm sure there will be none. Think about this when you're trying to save money (if that is a goal). Since you mentioned that this is your first experience with a machine shop, I am assuming that you haven't built engines before. I'm not trying to predict doom and gloom, but if you have no experience, don't have the necessary micrometers (and skills to use them), don't have the rest of the assembly tools that we all use, then are you asking too much of yourself from the get go? Consider working with a 'mentor' who has all of these things - to help you with your first build.
. Maybe you can arrange to be a 'fly on the wall' if they are putting it together. Being a 100% newbie (my assumption) - without tools and experience is asking for a bad experience (which none of us want you to have).
Balancing: I would make sure that the engine is balanced - is always a good idea for any engine build.
Parts to Bring: They should also be asking for the flywheel, the clutch, the timing cover, the oil-pan, etc.. There are things like camshaft end-play that need to be checked . . . which requires cam/crank gears and a timing cover . . . and the associated gaskets.
Also, do they (or you) have experience in selecting the various parts (and suppliers) they're going to put into it? There are quite a few suppliers for parts - some good, some okay and some poor . . . what parts are they using and who are they buying them from?
Make sure you buy some good Flathead Books - there are a handful that every beginner should have. Learn everything you can to plan your build . . . ask all the questions on the front end of the project.
Good luck!
B&S