Is it possible to get the output exported file with somehow modified format for the extracted fields? How can I customize such file?
If the built-in export variants from FlexiCapture 12 do not meet your needs and you want to customize the export output, then it is recommended to write your own custom export (either as a separate Export stage, or as a custom export script in the Document Definition).
Please find some samples of the export scripts - https://help.abbyy.com/en-us/flexicapture/12/developer/scripting_export_ex
The FlexiCapture objects available in the custom export can be combined with, for example, any appropriate .NET library that works with the output format you need, this way you will be able to customize the resulting file according to your needs.