For those that are looking for a way to create an srt or vtt file from Amazon Transcribe Service

CaptionAmazonService.php

<?php
//Not everything will work out of the box for you, as this is just for our application.
//Framework Laravel

namespace Modules\Caption\Services;

//https://github.com/captioning/captioning
use Captioning\Format\WebvttFile;
use ilos\Models\Caption\CaptionRequest;
use Exception;
use stdClass;

/**
 * Class CaptionAmazonService
 * @package Modules\Caption\Factories\Implementation
 */
class CaptionAmazonService
{
    /**
     * Paragraphs will be split in BLOCK_DURATION seconds
     */
    const BLOCK_DURATION = 2;
    /**
     *
     */
    const ITEM_TYPE_PUNCTUATION = 'punctuation';

    /**
     * @var WebvttFile
     */
    private $webvttFile;

    /**
     * CaptionAmazonService constructor.
     * @param WebvttFile $webvttFile
     */
    public function __construct(WebvttFile $webvttFile) {
        $this->webvttFile = $webvttFile;
    }

    /**
     * @param CaptionRequest $captionRequest
     * @param stdClass $contents
     * @return mixed|null
     * @throws Exception
     */
    public function createCaptionFileFromBlocks(CaptionRequest $captionRequest, stdClass $contents) {

        $duration = self::BLOCK_DURATION;
        $blockNumber = 1;
        $blocks = [];

        if(!isset($contents->results->items)){
            return null;
        }

        foreach($contents->results->items as $key => $item) {
            $isPunctuationItem = $this->isPunctuationItem($item);

            if(!$isPunctuationItem && $item->start_time > $duration) {
                $blockNumber++;
                $duration = $item->end_time + self::BLOCK_DURATION;
            }

            $isNewBlock =!isset($blocks[$blockNumber]);
            if($isNewBlock && !$isPunctuationItem){
                $this->initializeBlock($blocks, $blockNumber, $item);
            }

            $isPunctuationItem ? $this->updateSentence($blocks, $blockNumber, $item) :
                $this->updateBlock($blocks, $blockNumber, $item);
        }

        return $this->saveCaptionFileFromBlocks($captionRequest, $blocks);
    }


    /**
     * @param $blocks
     * @param $key
     * @param $item
     */
    private function initializeBlock(&$blocks, $key, $item) {
        $blocks[$key] = [
            'start_time' => [
                'seconds' => gmdate("H:i:s", $item->start_time),
                'milliseconds' => explode('.', $item->start_time)[1],
            ],
            'end_time' => [
                'seconds' => gmdate("H:i:s", $item->end_time),
                'milliseconds' => explode('.', $item->end_time)[1],
            ],
            'sentence' => '',
        ];
    }

    /**
     * @param $item
     * @return boolean
     */
    private function isPunctuationItem($item){
        return $item->type == self::ITEM_TYPE_PUNCTUATION;
    }

    /**
     * @param $blocks
     * @param $key
     * @param $item
     */
    private function updateSentence(&$blocks, $key, $item) {
        $sentence = $blocks[$key]['sentence'];
        #Removes whitespace from the end of the last word if the current word is punctuation
        $this->isPunctuationItem($item) ? $sentence = substr($sentence, 0, -1) : null;
        $blocks[$key]['sentence'] = $sentence.$item->alternatives[0]->content." ";
    }

    /**
     * @param $blocks
     * @param $key
     * @param $item
     */
    private function updateBlock(&$blocks, $key, $item) {
        $this->updateSentence($blocks, $key, $item);
        $blocks[$key]['end_time'] = [
            'seconds' => gmdate("H:i:s", $item->end_time),
            'milliseconds' => explode('.', $item->end_time)[1],
        ];
    }

    /**
     * @param CaptionRequest $captionRequest
     * @param $blocks
     * @return mixed
     * @throws Exception
     */
    private function saveCaptionFileFromBlocks(CaptionRequest $captionRequest, $blocks){

        foreach($blocks as $key => $block){
            $start = $block['start_time']['seconds'].'.'.str_pad($block['start_time']['milliseconds'], 3, "0", STR_PAD_RIGHT);
            $stop = $block['end_time']['seconds'].'.'.str_pad($block['end_time']['milliseconds'], 3, "0", STR_PAD_RIGHT);
            $this->webvttFile->addCue($block['sentence'], $start, $stop);
        }

        $this->webvttFile->build();
        $this->webvttFile->save($captionRequest->localStoragePath);

        return $captionRequest->localStoragePath;
    }
}