I do not believe you can turn off the startup/boot sound unless you had your sound set to silent before rebooting. Side note, I miss my old Droid boot sound. Only problem is that now you have no sound after boot unless you remember to turn it back on. I do know that after the first several Droids Motorola actually turned down the volume of the boot sound, which was done on mine after an OS update.
Thanks. I just upgraded from a Galaxy S3 to the Droid Turbo, and I am trying to get everything set like I had on the old phone. So far the Turbo is a HUGE improvement over the Galaxy, but the S3 was able to silence the startup sound.
I believe if you try Tikibar's suggestion in the link you might find your answer. I spoke too soon and while what I said is true in regards to silencing the sound during boot, my suggestion wasn't a long term solution.