There is an API to get results on a multiple zip codes API request:
Use this API to find out the city, state, latitude, longitude, and timezone information for multiple zip codes in one API. The JSON and XML responses contain alternative acceptable city names for a location. Send a GET request to:
Each zip code sent via API counts as a separate request. For example, if you send 5 zip codes, you will be charged for 5 requests. Any zip codes not found are not included in the response.
Read more about timezone returned: https://blog.zipcodeapi.com/zip-code-to-timezone-api/