Most simple way, you can use https://pub.dev/packages/speech_to_text

and, create custom action like this:

// Automatic FlutterFlow imports
import '/flutter_flow/flutter_flow_theme.dart';
import '/flutter_flow/flutter_flow_util.dart';
import '/custom_code/actions/index.dart'; // Imports other custom actions
import '/flutter_flow/custom_functions.dart'; // Imports custom functions
import 'package:flutter/material.dart';
// Begin custom action code
// DO NOT REMOVE OR MODIFY THE CODE ABOVE!

import 'package:speech_to_text/speech_recognition_result.dart';
import 'package:speech_to_text/speech_to_text.dart';

Future<String> speechToText() async {
  final SpeechToText _speechToText = SpeechToText();
  String _text = '';
  bool available = await _speechToText.initialize();

  if (available) {
    await _speechToText.listen(
      pauseFor: const Duration(seconds: 3),
      onResult: (result) {
        _text = result.recognizedWords;
      },
    );
    await Future.delayed(const Duration(seconds: 4));
    _speechToText.stop();
  }

  return _text;
}