TBH, whether or not the flat rate scheme is the best approach isn't something anyone here can honestly answer in a case like this: To decide you need to look at their figures and try to work out whether or not that's the case.

Noting that you say it's a voluntary registration due to expected growth, are they a new business, or one that has already been trading a while but still under the threshold?

If the latter, then you could look at their existing records and try to work out what their VAT liability might have looked like under the flat rate scheme compared to how it might have looked like on the other schemes. You won't get the exact figures for the latter unless you want to spend ages looking in detail - but you should be able to approximate it. (The flat rate scheme figure, on the other hand, should be very precise!)

If the former, you could guesstimate the figures based on cash flow projections - but given that projections for a new business are little more than (educated) guesswork, you can see why I said "guesstimate" rather than "approximate".

Otherwise, it's a case of suck it and see: As you do the bookkeeping going forward, keep a track of what the VAT would look like if they weren't on the scheme, and compare with what they're actually paying.