React Native Speech to Text
You might wanna look at react-native-android-voice, a React Native module that supports speech-to-text for Android.
As @delkant mentioned, there's now also react-native-voice that supports both Android and iOS.
Alternatively, you can always write your custom native module using Android's SpeechRecognizer API. Here's a summary of all the classes and interfaces you might need for this task. If you are familiar with developing native Android apps, it's pretty easy to create a native module and bind it to your React Native project. Here's the official documentation of how to achieve this.
You also have react-native-voice
A speech-to-text library for React Native.
It supports android and iOS