Hello Rachel Keeley, 

Welcome to the Community page, 

So customers who are on and using the Flat Rate Scheme, is not supported under the CIS DRC. You will need to discuess your options with your accountant and ultimately HMRC to move away from FRS. Reverse charge supplies are not to be accounted for under the scheme. Flat Rate Scheme users who receive reverse charge supplies will have to account for the VAT due to HMRC and recover it simultaneously on the same VAT Return.
Users of the Flat Rate Scheme will have to consider if it’s still beneficial to them bearing in mind that under the scheme they cannot recover VAT incurred on purchases of materials, overheads and so on.(Reference section 13- https://www.gov.uk/guidance/vat-reverse-charge-technical-guide#flat-rate-scheme)