you can try the following:
1. add user/password in /etc/ppp/{chap,pap}-secrets
2. in "/etc/ppp/peers/peer-3" comment line "noauth"
3. add line (username to use for authentication, should match "client" in /etc/ppp/{chap,pap}-secrets):
user "change_this_to_your_username"
you can also try to modify "peer-4" and "connect-4" according to your GSM provider, because kindle could use those files for connecting. I'm not sure how it chooses which peer/connect number to use
if that don't help, you can turn on pppd debug mode and see whats going wrong. to enable debug mode enter these two lines in "/etc/ppp/peers/peer-3":
--------
debug
logfile /mnt/us/pppd_log.txt
-------
then try to restart/connect to gsm network and read the log file.