I found the following web page that details how to install Flash in FreeBSD without using the Linux compatability layer:

http://www.riondabsd.net/2007/05/23/flash-on-freebsd-using-gnash/

That page is slightly out of date; there is a new version of Firefox, for one thing.  Basically, the procedure is to install the following ports:

www/firefox35
graphics/gnash
multimedia/mplayer
www/mplayer-plugin

Then you have to install the GreaseMonkey plug-in, and then a special GreaseMonkey script.

Unfortunately, the GreaseMonkey script referenced on that page is out-of-date; it looks like YouTube has updated their web site and changed some of the object IDs.  Once I work out a working script, I'll post it here.

EDIT: After tinkering around with GreaseMonkey a bit, I realized that YouTube videos were working without the GreaseMonkey script!  It often takes a while for the player to kick in, but I am indeed able to watch YouTube videos with no GreaseMonkey script at all.  The audio is about 0.75 seconds behind the video, but hey beggars can't be choosers!  :)