There is no way you can view disappearing photos or videos after you've sent them. However, you can see if they were delivered, opened, replayed or if someone took a screenshot of them. Once you've sent a disappearing photo or a video to someone, you can see the conversation as a circle at the top of your inbox. You'll see 'a tick mark in a white circle' icon below the messages that have been delivered and 'a tick mark in a gray circle' icon below messages that have been opened.
If Instagram detects that your message was replayed or screenshotted, you can also see that from the top of your inbox. If you sent a message to one person, you'll see the status of that message below the conversation (ex: Replayed, Screenshot). For group conversations, tap and hold the conversation and select 'View Activity'. From there, you'll see the status of your message with each person in the group.
Keep in mind that you'll only see the status of your messages right after you've sent them. For example, if someone replies to your message in a group conversation, you'll no longer be able to see the status of the original message you sent.