The only way to find your Boost Mobile account number is to call Boost customer support at 1-888-266-7848. The number is not listed in your online account.
When you call the customer support number, you'll need to speak to a live representative. This is the quickest way to reach someone, as of 2015: first, enter your Boost phone number with area code, then press 4 for "Technical Issues." After listening to the next set of menu options, wait ten more seconds and you'll be prompted to press 0 to reach a Boost customer care representative. You'll also need to enter your 4-digit PIN before being connected.