Question

Is there a SOAP API available in the FlexiCapture SDK version

Answer

FlexiCapture SDK does not include an out-of-box web API. But it is quite simple to develop your own API interface. You will need to create an authentication module and forward access to some methods. It can be a Tomcat-based application or ASP.NET, etc.

More information about this you can find here:
https://help.abbyy.com/en-us/flexicapturesdk/12/user_guide/guidedtour_fcengineguide_overview/ 
https://help.abbyy.com/en-us/flexicapturesdk/12/user_guide/guidedtour_samples/

It all depends on your needs. FlexiCapture SOAP API may be sufficient or not:
https://help.abbyy.com/en-us/flexicapture/12/developer/references/