Hi I got the same issue… please help someone 

Hi @Ksenia and @Niels Timmerman, welcome! Strange that it's not working! I receive texts from Instagram/Facebook fine with my KPN simcard, but I use a Samsung phone without esim. Did you receive texts from Instagram before? Or is this the first time you've tried? I found some advice on the internet: have you tried using an incognito browser? Do you use VPN? Did you try to restart your device? If it's still not working you could ask Instagram if they can help you fix the problem.

I tried incognito and other things, it didn’t help. At some point Instagram let me in and add another way of two-factor authentication - by the app. So I can use Instagram. But I still don’t receive any sms messages from them.

Sometime is there a delay in the SMS-traphic. Have patience or try again later.

Why you use SMS and not 2FA with a auth-app?

Most reliable. 

Because Instagram forced me to enter code from sms and nothing else was available!

After they let me in normally, I added 2FA with an auth-app.

how did they let you in? did you contact instagram?

I have the same problem