I have the same problem with Opera 9.61 (flash won't load). Later I found that the real problem is flash10 needs libnss3.so, which is provided by firefox but not opera.
I updated /etc/ld.so.conf to add:
And then run (as root):
After that, Opera can load flash without problem.
I'm not on my slackware box right now, so I'm not quite sure about the directory name
Please verify before you make change. I should also mention I'm using -current.