Most International/European (expat) insurances cover chiropractic care and also the technical exams.
For the Dutch insurance you need to be complementary insured (aanvullend).
Then it will be fully/partially covered depending on the package you took.
Chiropractic care will NOT be claimed by your OWN RISK.
Referral from your GP is not necessary.
Here is the link for an overview of the dutch insurancecompanies and their different packages chiropractievergoeding