Survey.jsx

import React from "react"
import { NativeModules } from "react-native"

const SurveyManager = NativeModules.SurveyManager

class Survey extends React.Component {
    componentDidMount() {
        SurveyManager.start({ ... }, prompt => {
            this.setState({ prompt })
        })
    }

    render() {
        if (!this.state.prompt) {
            return null
        }
        return (
            <View>
                <Text>{this.state.prompt.question}</Text>
                <Button title="Next question" onPress={() => SurveyManager.nextScreen(true) } />
            </View>
        )
    }
}

SurveyManager.m

@interface SurveyManager : NSObject <OFISurveyHandlerDelegate>
@property (strong) RCTResponseSenderBlock showNextScreenCallback;
@end

@implementation SurveyManager

RCT_EXPORT_METHOD(start:(NSDictionary *)surveyOptions
             completion:(RCTResponseSenderBlock)showNextScreenCallback
{
    self.showNextScreenCallback = showNextScreenCallback;

    OFFloodgateOptions *options = [[OFFloodgateOptions alloc] init];
    options.surveyHandlerDelegate = self;
    // ...
    [OfficeFloodgate initWithOptions:options];
    [[OfficeFloodgate getEngine] start];
}

- (void)showPrompt:(id<OFIPrompt>)prompt
{
    self.showNextScreenCallback(@{
        @"question": prompt.question,
    });
}

RCT_EXPORT_METHOD(nextScreen:(BOOL)showNextScreen)
{
    [prompt presentNextScreenForSelectedButton:showNextScreen ? OFPromptButtonYes : OFPromptButtonNo];
}

@end