As far as I know, there is no direct support for uploading multipart form data in the JAX-RS client. But by using the MultipartEntityBuilder from the Apache HTTP Client within a JAX-RS StreamingOutput, it is possible to do a multipart form data upload from a JAX-RS client with only some lines of code:
import java.io.File;
import java.util.UUID;
import javax.ws.rs.client.*;
import javax.ws.rs.core.*;
import org.apache.http.HttpEntity;
import org.apache.http.entity.ContentType;
import org.apache.http.entity.mime.MultipartEntityBuilder;
public class MultipartJaxRsClient {
    public static void main(String[] args) {
        // prepare MultipartEntityBuilder:
        String boundary = "-----------" + UUID.randomUUID().toString().replace("-", "");
        MultipartEntityBuilder entityBuilder = MultipartEntityBuilder.create().setBoundary(boundary);
        // add file(s):
        String multipartFieldName = "file1";
        File fileToUpload = new File("test.pdf");
        ContentType contentType = ContentType.create("application/pdf");
        entityBuilder.addBinaryBody(multipartFieldName, fileToUpload, contentType, fileToUpload.getName()).build();
        // ... add more files ...
        // wrap HttpEntity in StreamingOutput:
        HttpEntity entity = entityBuilder.build();
        StreamingOutput streamingOutput = out -> entity.writeTo(out);
        // use StreamingOutput in JAX-RS post request:
        WebTarget target = ClientBuilder.newClient().target("http://server/path/to/upload");
        String multipartContentType = MediaType.MULTIPART_FORM_DATA + "; boundary=\"" + boundary + "\"";
        Response response = target.request().post(Entity.entity(streamingOutput, multipartContentType));
        System.out.println("HTTP Status: " + response.getStatus());
    }
}
The above code was tested with Apache HTTP Client 4.5.13 and Apache CXF 3.5.4 JAX-RS client:
<dependency>
    <groupId>org.apache.httpcomponents</groupId>
    <artifactId>httpmime</artifactId>
    <version>4.5.13</version>
</dependency>
<dependency>
    <groupId>org.apache.cxf</groupId>
    <artifactId>cxf-rt-rs-client</artifactId>
    <version>3.5.4</version>
</dependency>