использование клавиатуры AvoidingView от 'Reaction-native'
документы
import {
KeyboardAvoidingView
} from 'react-native';
<KeyboardAvoidingView behavior="padding" style={styles.container}>
<View style={styles.inputContainer}>
<TextInput
returnKeyType="next"
placeholder="Mobile No."
placeholderTextColor="powderblue"
keyboardType="number-pad"
onSubmitEditing={() => this.passwordInput.focus()}
style={styles.input}
onChangeText={(value) => this.setState({mobileno:value})}
value={this.state.mobileno}
/>
<TextInput
returnKeyType="go"
placeholder="Password"
placeholderTextColor="powderblue"
style={styles.input}
secureTextEntry
ref={input => (this.passwordInput = input)}
onChangeText={(value) => this.setState({pssd:value})}
value={this.state.pssd}
/>
</View>
</KeyboardAvoidingView>