some observations for your consideration:
Although USPS has different sizes of flat rate boxes available, it is treacherous to enable those for customer shipping. Customers have no idea what size box their order will fit into, and will usually select the lowest cost of the offerings (no surprise there). We suggest that you can offer First class and Priority Mail. The USPS will only show the selections that are available to your customers based on the weight of the total order. First class packages as defined by USPS rules must be under 15.99 ounces for the rate to come up as a selection.
I am unsure which Flat rate you are offering - the system flat rate or some of the USPS flat rates. With more details, we can probably get closer to getting you a good solution.