项目中是服务端持有私钥，客户端持有公钥；
客户端使用公钥加密，并使用公钥解密服务端 用私钥加密的数据。

网上相关的资料实在再少，终于功夫不负有心人，被我找到了。附上代码。

先引入包 ：
https://pub-web.flutter-io.cn/packages/encrypt
https://pub.dev/packages/pointycastle

encrypt: ^5.0.1
pointycastle: ^3.1.1

import 'dart:convert';
import 'package:encrypt/encrypt.dart';
import 'package:flutter/services.dart';
import 'package:pointycastle/api.dart';
import 'package:pointycastle/asymmetric/api.dart';
import 'package:pointycastle/asymmetric/pkcs1.dart';
import 'package:pointycastle/asymmetric/rsa.dart';
// import 'package:pointycastle/export.dart';

class EncryptUtil {

  // Rsa加密最大长度(密钥长度/8-11)
  static const int MAX_ENCRYPT_BLOCK = 245;

  // Rsa解密最大长度(密钥长度/8)
  static const int MAX_DECRYPT_BLOCK = 256;

  //公钥分段加密
  static Future encodeString(String content) async {
    //加载公钥字符串
    final publicPem = await rootBundle.loadString(这里写密钥路径);
    //创建公钥对象
    RSAPublicKey publicKey = RSAKeyParser().parse(publicPem) as RSAPublicKey;
    //创建加密器
    final encrypter = Encrypter(RSA(publicKey: publicKey));

    //分段加密
    // 原始字符串转成字节数组
    List<int> sourceBytes = utf8.encode(content);
    //数据长度
    int inputLength = sourceBytes.length;
    // 缓存数组
    List<int> cache = [];
    // 分段加密 步长为MAX_ENCRYPT_BLOCK
    for(int i=0;i<inputLength;i+=MAX_ENCRYPT_BLOCK){
      //剩余长度
      int endLen = inputLength-i;
      List<int> item;
      if(endLen > MAX_ENCRYPT_BLOCK){
        item = sourceBytes.sublist(i,i+MAX_ENCRYPT_BLOCK);
      }else {
        item = sourceBytes.sublist(i,i+endLen);
      }
      // 加密后对象转换成数组存放到缓存
      cache.addAll(encrypter.encryptBytes(item).bytes);
    }
    return base64Encode(cache);
  }

  //公钥分段解密
  static Future decodeString(String content) async{
    //加载公钥字符串
    final publicPem = await rootBundle.loadString(这里写密钥路径);
    //创建公钥对象
    RSAPublicKey publicKey = RSAKeyParser().parse(publicPem) as RSAPublicKey;

    AsymmetricBlockCipher cipher = PKCS1Encoding(RSAEngine());
    cipher.init(false, PublicKeyParameter<RSAPublicKey>(publicKey));

    //分段解密
    //原始数据
    List<int> sourceBytes = base64Decode(content);
    //数据长度
    int inputLength = sourceBytes.length;
    // 缓存数组
    List<int> cache = [];
    // 分段解密 步长为MAX_DECRYPT_BLOCK
    for(var i=0;i<inputLength;i+=MAX_DECRYPT_BLOCK){
      //剩余长度
      int endLen =inputLength - i;
      List<int> item;
      if(endLen > MAX_DECRYPT_BLOCK){
        item = sourceBytes.sublist(i,i+MAX_DECRYPT_BLOCK);
      }else {
        item = sourceBytes.sublist(i,i+endLen);
      }
      //解密后放到数组缓存
      cache.addAll(cipher.process(Uint8List.fromList(item)));
    }
    return utf8.decode(cache);


  }
}

参考资料：
https://stackoverflow.com/questions/61858252/flutter-how-to-decrypt-a-rsa-private-key-encrypted-string-if-we-have-rsa-publi
https://github.com/leocavalcante/encrypt/issues/180
https://www.jianshu.com/p/0194b99a4b3d