You can now add up to 5 Instagram accounts and quickly switch between them without having to log out and log back in. This is included on version 7.15 for iOS and Android, available in the App Store and the Google Play Store.
To add multiple Instagram accounts:
● Go to your profile and tap the settings icon at the top right
● Scroll down and tap Add Account
● Enter the username and password of the account you'd like to add
To switch between accounts you've added:
● Go to your profile
● Tap your username at the top of the screen
● Tap the account you'd like to switch to
You can download Instagram from the App Store for free.