File Management

iOS devices like iPhone's do not have a traditional file system like computers. THere is no traditional file management on it. As such any downloads will not be visible anywhere else but in the browser used to download them.

On iOS devices, all apps must reside within an App. However, there is no native Zip management App or option in iOS, so the file cannot be transferred anywhere except those Apps you sited that have registered themselves as being able to manage zip files and as such will appear in the Open With dialog.

To manage things like Zip files you need to have an App than can open and view them. I would suggest something like Documents by Readdle, or File Manager. both are free and can handle Zip files. They will register themselves in the Open In / With dialog and will let you transfer the zip file to them, so you can open it and view the files inside.

‎Documents by Readdle on the App Store

‎File Manager & Browser on the App Store

I would check iPhones local file management in the "Files" app. Its possible that you saved it to your phone, or iCloud account when you downloaded it. As a general rule, saving limited downloads to your phone is probably a bad idea. It would be better to save it to your Mac, then transfer it over after.