It could be caused from a) your IP adress or b) your device. Give a try on another internet provider (could be 4g rooting from some friend, or shopping public wifi) to see what happens. Also try another device and see what happens. If you found that the problem is with your device, here in this forum theres some people talking about reset the id of any device, try it.
btw, may nothing of this will help you. Instagram is really stuck in this bug, and theres no reason why. Another people are talking about infinite verification too… 1 Account Comprmised loop 2 Infinite loop "Help us confirm you own this account" 3 Impossible Instagram Verification Loop
Some days ago this happens to me too, all that I did was wait for some ten days. Now its ok.