Instagram no longer has an Apple Watch application. The Verge can confirm that the update of version 39.0 to the iPhone client, which comes with a change log that simply indicates "bug fixes and performance improvements", completely eliminates the Watch application.
As 9to5Mac points out, this is likely due to a new restriction that Apple is imposing. As of April 1, updates to Apple Watch applications should use the watchOS SDK 2 or later, while new Watch apps should be created with the watchOS SDK 4. The Instagram application goes back to the days of WatchKit 1.0, when third-party software could not run natively on the clock; never got features such as video support or the ability to work over an LTE connection.
To complete the compatibility with your Apple Watch application, Instagram follows other prominent companies such as Twitter, Google, Amazon and Slack. Many have discovered that good notification support is that all people really need or want to be out of Watch's functionality, and in some cases eliminating the application has even resulted in usability improvements. But since the Instagram application focused on recreating the same scrollable content of the full version of the phone, his death is a strong signal that the social network does not consider Apple Watch to be an independent and useful application platform.