I have not found an effective way to stretch chest without flaring up nerves in the arms.
The only stretch that kind of worked is to lie on the back and have someone pin your shoulders to the floor. Don't know how effective it is though.
As my nerves calmed down, it became easier to stretch. It took a year or so, but I can now do the doorframe stretch almost without pain in the arms.
In my case I am sure that the neck is the source of the problem so chest stretches don't do much...