I didn't have any problem. Possible stupid question, but you placed the balloons in Krustyland, right? You aren't talking about the limited-time balloons that were available in Springfield?
I didn't buy balloons until prompted, but I had more than ten flowers in storage when the place flowers quest poped up for part 3. I'd guess it should prompt if you place all your balloons in storage, and then click through the task bar icon it'll take you to your inventory to place the balloons. I don't think it'll trigger if you place the balloons from the box icon.
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