You must pass the string[] parameter as a repeated URL parameter.
API call example
http://<AddressManager_IP>/Services/REST/v1/customSearch?filters=filter1=abc&filters=filter2=def&type=IP4Block&options=&start=0&count=10
Authorization: BAMAuthToken: UTtSjMTQ1ODAzMTgzMDUxMzphcGk=
Content-Type: application/json
Successful response
Returns a list of results based on the filter criteria.