What you're doing is using your Flex as a code practice oscillator. While that will work, you're using a lot of expensive equipment for something that can be accomplished with some very inexpensive and very portable circuitry.
If you do need to use your Flex, then use a dummy load and turn the power output down to nothing. That will get the job done and everything will operate exactly as it does on the air. Otherwise, look for a keyer or code oscillator that you can set up at the kitchen table or anywhere else you want to practice. Google will yield a bunch of them, but here's one from MFJ that should work for around fifty bucks.
Rob, the Flex has an internal iambic keyer for use with a paddle which is selected by clicking "On" the Iambic button. If you do not select the Breakin button, the rig will not go into transmit but can be used as a practice oscillator with the internal keyer.
If you want to use either an external keyer or a straight key for practice, do not select either the Breakin or the Iambic buttons. If you want to transmit with your straight key or with your external keyer, just select the Breakin button.
As has already been said, its a good idea to use a dummy load rather than leave the rig connected to an antenna.
Good luck with the practice, do it little & often