To delete an Instagram draft, go to “+” → Post → Drafts, tap Manage, then Edit, select the drafts you don’t want, and hit Discard Posts. That’ll remove them permanently.
To delete an Instagram photo from drafts, open Instagram, tap the “+” icon, then Drafts. Tap Manage, select Edit, choose the draft you want to remove, and tap Discard Post.
In order to remove an Instagram photo draft, press the plus symbol, enter the drafts area, pick "Manage," then "Edit" to select and delete the posts you wish to get rid of.