I have a (crude) working piece of code
// web/index.html

<script src="../lib/wallet.js" />

// wallet.js

class ClientWallet {

    constructor() {
        this.pubKey = '';
    }

    async connect() {
        const resp = await window.solana.connect();
        this.pubKey = resp.publicKey.toString();
    }

    address() {
        return this.pubKey;
    }

    disconnect() {
        window.solana.disconnect();
    }
}

var walletModule = { ClientWallet: ClientWallet };

// main.dart

import 'package:js/js.dart';
import 'package:js/js_util.dart';

@JS('walletModule.ClientWallet')
class ClientWallet {
  external Future<void> connect();
  external void disconnect();
  external String get pubKey;
}

Future<void> connectWallet() async {
  ClientWallet wallet = ClientWallet();
  await promiseToFuture(wallet.connect());
}

And then for connecting simply call connectWallet(). This works for me for the Phantom wallet.
EDIT: To accomplish this I went to the docs for connecting a Phantom wallet . I also had to use Dart-JS interop to make it work.

目前还没有办法做到这一点，除非存在一个额外的外部包。最好的办法可能是将wallet绑定添加到community Dart包中：https://github.com/cryptoplease/cryptoplease-dart

你可以用我的包flutter_phantom
这是签名和发送事务示例

Future<web3.Transaction> createTransactionTransfer() async {
   final transaction = web3.Transaction(
  feePayer: phantom.phantomWalletPublicKey,
  recentBlockhash: (await connection.getLatestBlockhash()).blockhash);
 transaction.add(
   SystemProgram.transfer(
    fromPublicKey: phantom.phantomWalletPublicKey,
    toPublicKey: phantom.phantomWalletPublicKey,
    lamports: web3.solToLamports(1),
   ),
   );
return transaction;
}

 void signAndSendTransaction() async {
  try { 
   web3.Transaction transaction = await createTransactionTransfer();

   web3.Buffer transactionSerialize = transaction
    .serialize(const web3.SerializeConfig(requireAllSignatures: false));

final url = phantom.generateSignAndSendTransactionUri(
    transaction: transactionSerialize,
    redirect: "onSignAndSendTransaction");

launchUrl(
  url,
  mode: LaunchMode.externalNonBrowserApplication,
);
 } catch (e) {
 print(e)
  }
 }

如何使用此软件包flutter_phantom-demo完整示例