We have around 6 individual REST services which we would be calling in our orchestration layer. for example "Calling service-1 to check if a bank account is of certain type, if yes, then call service-2, else call service-3".
Is Spring Integration messaging framework is a right tool for orchestrating calls to those services or its an overkill? Please suggest if there is a better way to accomplish the same.
I can't suggest you better tool, because Spring Integration was the best one for me in the past and now it is my full time job. So, try to find other answers somewhere else.
Now about the point of orchestration
with the Spring Integration. To be honest it's just a word which tries to describe the business logic in one application when it calls other external application according some conditions.
So, from big height having HTTP adapters in the Spring Integration, Transformers, Splitters, Routers and Gateways between them, we can say with confidence that messaging layer on Spring Integration fits your requirements and really can help you to distinguish business logic from the orchestration logic.
Not sure what to say else, but I can recommend take a look to the Spring Integration Reference Manual and pay attention to the Routing Slip
and Scatter-Gather
patterns.