Instagram search by phone number, by using a phone number, you can easily find an Instagram account with it.
Lets see the steps to guide on how you can easily find someone by phone number.

First open the instagram app on your phone or devices
Then click on the profile picture icon at the bottom right corner
Tap on the three line icon at the top settings.
Click the account from the settings. Then scroll down and then click contact syncing.
Then enable the button to sync up the phone number on your devices to your instagram. Then you will be asked to allow instagram to access your contacts.
Then go back to the instagram profile page. You can see the several contacts there and follow them.