I used to use the security token that I bought for use with FF XI, but I switched over to the phone app on Android when that came out and it's worked perfectly fnie for me (for like 3 years now?)

One phone I had broke and I couldn't use the code any more, but I'd made a note of the emergency removal password like they said so it was easy to remove it and then set it up again on my new phone.

As long as you have the removal password safe somewhere, it doesn't matter what happens to your phone, you'll be able to remove the token from your account without involvement from SE.