Unfortunately, you can only unlink your Facebook account from your Instagram through the Instagram app. The two accounts cannot be unlinked through Facebook.
Open the Instagram app. Navigate to the upper-right corner of your profile and click the icon with three lines. Select “settings,” and then “account,” then go to “accounts center.”
Here it will display all of the accounts you have linked to your Instagram, including Facebook, Twitter, Tumblr, among others.
A username will be displayed next to any Facebook account that is linked to your Instagram. Select “Facebook,” and then click “Unlink account.” You’ll have to confirm this on a pop-up before the action is completed, but once you confirm it, your two accounts will no longer be linked together.
You can also delink other Instagram accounts here.