HTTP API Path contain Chinese response 409 path not found?

Your code sample uses some custom classes so I can't run it, but this runs fine for me:

import java.io.ByteArrayOutputStream;
import java.io.IOException;
import java.io.OutputStream;

import com.fasterxml.jackson.core.JsonFactory;
import com.fasterxml.jackson.core.JsonGenerator;
import org.apache.http.HttpEntity;
import org.apache.http.HttpResponse;
import org.apache.http.client.ResponseHandler;
import org.apache.http.client.methods.HttpPost;
import org.apache.http.impl.client.CloseableHttpClient;
import org.apache.http.impl.client.HttpClients;
import org.apache.http.util.EntityUtils;

public class Main {

    public static void main(String[] args) throws IOException {

        String ACCESS_TOKEN = "<ACCESS_TOKEN>";
        String filePath = "/blackdog/中文prd.docx";

        JsonFactory jsonFactory = new JsonFactory();
        OutputStream outputStream = new ByteArrayOutputStream();
        JsonGenerator jsonGenerator = jsonFactory.createGenerator(outputStream);
        jsonGenerator.setHighestNonEscapedChar(0x7E);
        jsonGenerator.writeStartObject();
        jsonGenerator.writeStringField("path", filePath);
        jsonGenerator.writeEndObject();
        jsonGenerator.close();

        String arg = outputStream.toString();
        System.out.println(arg);

        CloseableHttpClient httpclient = HttpClients.createDefault();
        try {
            HttpPost httpost = new HttpPost("https://content.dropboxapi.com/2/files/get_preview");
            httpost.setHeader("Authorization", "Bearer " + ACCESS_TOKEN);
            httpost.setHeader("Dropbox-API-Arg", arg);

            ResponseHandler<String> responseHandler = new ResponseHandler<String>() {

                @Override
                public String handleResponse(final HttpResponse response) throws IOException {
                    int status = response.getStatusLine().getStatusCode();
                    System.out.println(status);
                    HttpEntity entity = response.getEntity();
                    return entity != null ? EntityUtils.toString(entity) : null;
                }
            };

            String responseBody = httpclient.execute(httpost, responseHandler);
            System.out.println(responseBody);

        } finally {
            httpclient.close();
        }

    }
}

That outputs:

{"path":"/blackdog/\u4E2D\u6587prd.docx"}
200
%PDF-1.4
%Ç쏢
<more PDF content truncated for brevity>