In the Distributed version of FlexiCapture, usage of the absolute paths (for example, C:\Temp) as the Export destination is prohibited. So it is needed to specify the network folder (for example, \\localhost\\Export) as the Export destination if you are configuring Export to files.
For this network folder, the full access rights (Read and Write) should be given to the process that runs the export. In the ABBYY FlexiCapture 12 Distributed it is the Processing Station process - FlexiBrSvc.exe.
By default, this service runs from the name of the Network Service, but if it's changed, you can check what account is used in Services > ABBYY FlexiCapture 12 Processing Station > Log On tab: