Is it safe to copy the binlogs from a running mysql server I want to backup a tokudb database. 

I want to be able to restore it to the most recent state. 
Which I am writing to a file at backup.

My guess would be to run something like this

mysql -e "SHOW MASTER STATUS; SHOW SLAVE STATUS; FLUSH LOGS" &gt; mylogposition.log


Which will rotate the log files after saving the position?
As long as you have done flush logs and you have taken the logfilename just before flush logs say it should be fine. 

Example current binlog file is bin-log00333 and after flush logs it is bin-log00334. You may scp the logs from bin-log00001 to bin-log00333 and don't take bin-log00334.