I'm using the package sms_maintained. refer to package for latest version.
Code sample from package.
import 'package:sms/sms.dart';
void main() {
  SmsSender sender = new SmsSender();
  String address = someAddress();
  ...
  sender.sendSms(new SmsMessage(address, 'Hello flutter!'));
}
I't provides other methods as well.
Querying, filtering, contact info, receiving and deleting as well.
For sending the a sms you'd need the necessary permissions.
And for other functionalities.
- RECEIVE_SMS 
- READ_SMS 
- READ_CONTACTS 
An extensive list of them are located here.
flutter AndroidManifest.xml is location => android/app/src/main/AndroidManifest.xml
EDIT #:
The package is no longer maintained. you may manually link to files from this repo
pubspec.yaml
dependencies:
  ...
  sms_maintained:
    path: plugin_folder_path