You can access Instagram on an Apple Watch, but not through the Instagram app.
How to Get Instagram and Facebook on Apple Watch
This article explains how to use the third-party Lens for Watch app to bring Instagram scrolling, liking, commenting, searching, and more right to your wrist. The Lens for Watch app requires an iPhone or iPad running iOS 12.0 or later and watchOS 4.0 or later.
Before you download the Lens for Watch app, make sure you’ve already paired your iPhone with your Apple Watch. Lens for Watch has a free version, but some features are only available in the $1.99 Pro version.
Download and install Lens for Watch on your iOS device, then select Open to launch the app.