Is this surgical tubing good for a slingshot?

Any elastic material that can be sized, won't tear or break when it is stretched, and will actually work in your slingshot is fine. Yes, rubber cracks. In fact, everything cracks. The question is how long will it take. Well, probably you'll grow tire of your slingshot before the rubber cracks...and if you don't, by then you'll have found another source of supply.