This facility is permanently unavailable on Instagram. You can only search friend with your Facebook account and phone number. Instagram give a specific username to the user so you can search your friend faster.
To find out with Facebook and contacts, open your app. Tap on the profile tab. Tap on the three bars in the right corner. Now tap the discover people option. Now you can search your Facebook friends on Instagram. It’s very simple.
If your friends whose number saved in your phone and he/she is an Instagram user, then you can search easily in contact. Swipe left to see contact option.