OK, so using your example you have:
Flame out hops,
10 minute steep
1st whirlpool hop addition
20 minute steep
2nd whirlpool hop addition (knockout?)
10 minute steep
I am assuming (for right or wrong) that you do not remove the hops (as in a hop bag) from one step to another.
So, your first flame out hops should be added as whirlpool hops for a total of 40 minutes (10 +20 +10 minutes for total steeping time)
Your second whirlpool hops will be added for 30 minutes (40 minutes minus the 10 minutes for the first addition)
Your third addition would be added for 10 minutes (40 minutes minus the 30 minutes which have already passed)
For temperatures, I would start with using the temperatures that you measure (if you have done so previously), or set if you have a HERMS system, or estimate from a reasonable idea of the temperature drop during the period of time from flame out to chilling. You can later go back and adjust the temperatures to correlate your sensory evaluation of bitterness to the calculated IBU number to bring them into alignment with your experiences.
For those hops which are added prior to turning the heat off, there is a setting in your equipment profile for 'estimate boil hop util in whirlpool' which you can check and then enter the full time of the whirlpool in the 'total whirlpool time' above that setting. This will extend the estimate of bittering realized from your boil hop additions for the added time of the whirlpool.
Just to throw another possibility at you, I had to stop the timer between flame out and first whirlpool hop addition due to the time it took me to grab volume and gravity sample. It would take me about 5 minutes from end of boil until I threw in my first hops. Later, I extended that to around 10 minutes for the addition of my immersion chiller and time to cool the wort to around 195F.
So, I made a 'dummy hop' called 'whirlpool pause' which contributes zero IBU. I add this in with the full timing from flame out to end of whirlpool.
So for instance, if you flame out hops above actually was added at 10 minutes after the end of the boil, I would add the 'whirlpool pause' for 50 minutes (10 minute pause + 40 minutes total time from above). This sets the timer in BeerSmith to give me the proper time to the first whirlpool addition without having to fuss around pausing the timer.
Hope this helps!