QuickFile will do most of the leg work for you. You would create your invoices as normal with the standard rates of VAT (e.g. 20%).
When you file your return QuickFile will calculate your Flat Rate Turnover and apply your lower Flat Rate percentage (e.g. 13%) against this figure. You can then review your VAT return, download and check a backing report (i.e. to see what is making up the totals) and submit electronically to HMRC.
I will leave this thread open for anyone else to comment.