Steps

Go to Settings → Connect Social Media.
Select the platform you want to connect.
Start with Instagram.
Log in through Facebook when prompted. Instagram can only be connected through Facebook.
Select the correct Facebook Page and Instagram account. A Facebook Page is not the same as your Facebook account. Your Instagram account must be associated with a Page created from your Facebook account.
Approve all permissions.
Repeat the process for YouTube and TikTok.
Confirm that all platforms show as Connected.

Important Notes

Your Instagram must be a public Creator or Business account, linked to a Facebook Page. It doesn't matter how many followers or how much activity the Page has; what matters is the data of your Instagram account.
Not sure what a Facebook Page is or how to link it? See Instagram Won't Connect: Facebook Page Requirements and Fixes.
Do not select “Invalidate another way” during the process.
Influur only accesses analytics, never your private messages or content.

Wrong Facebook account selected
Instagram not linked to a Facebook Page
Instagram is a personal or private account (it must be a public Creator or Business account)
Permissions not fully accepted