There's no one-size-fits-all answer to this question, as the amount of money you'll need to save to start an insurance agency will vary depending on a number of factors, including the type of insurance agency you want to start, the location in which you'll be operating, and the amount of start-up capital you have available. However, as a general rule of thumb, you should aim to have enough money saved up to cover at least six months' worth of operating expenses - that way, even if your business doesn't take off as quickly as you'd hoped, you'll still have enough cash flow to keep things going until it does.
Of course, how much money you actually need will also depend on how frugal you're willing to be when starting out. If you're comfortable working from home and forgoing some of the more traditional (and expensive) office set-ups and overhead costs associated with running an insurance agency, then your start-up costs will be lower than someone who wants to lease space for a brick-and-mortar agency right off the bat.
Ultimately, there's no magic number when it comes to how much money you should save before starting an insurance agency - but by carefully planning your expenses and knowing exactly what your needs will be upfront, you can ensure that you have enough cash on hand to get your business off the ground successfully.