Engine flushes are horrible ideas. No don't add a heavy solvent that will clunk any debris and deposit them into your filter, and worse the detergents some flushes use are down right harmful as they have a sand paper effect. Your amsoil will clean all by itself, and will not tarnish or sludge as easy as conventional oil. I would get the oil and do it myself the first time. Let the oil get a good drain, and then just add your amsoil and change the filter.
I looked up Amsoil flush, it has a very low flash point which leads me to believe it has a very high solvent base. really pass on this stuff. Amsoil Flush Flashed in closed cup at 275F compared to Autorx which flashes in open cup at 410F.
There is a flush that allows for a slow removal of debris, called autorx. it is very detailed, and if I was to do a flush that would be the type. It isn't done with solvent or detergents, but rather esters which are similar to what you find in synthetic oil anyway. But again, I would just make the switch with no flush, your Amsoil is awesome and will clean and lubricate by itself.
You are smart for asking before just doing it.
.