As of now, no social media management platform (Statusbrew included) can synchronize Instagram Direct Messages or DMs since this functionality is currently not available in their API.
Instagram's terms of service do not allow any tool to pull DMs through their API, any tool offering this feature isn't compliant with Instagram's TOS and can lead to an account ban.
Instagram has recently started offering private messages on desktop, so if in future Instagram does enable the option to sync DMs, we'll be implementing this feature in our Engage inbox.