Try running the following 'ldd <path to libflashplayer.so>', i.e. if you have 'libflashplayer.so' installed in '/usr/lib/mozilla/plugins' then type this:
$ ldd /usr/lib/mozilla/plugins/libflashplayer.so
You should receive some results back. What you are looking for is any lines that state 'not found', e.g.:
libnss3.so => not found
libsmime3.so => not found
libssl3.so => not found
libplds4.so => not found
libplc4.so => not found
libnspr4.so => not found
If you are receiving 'not found' lines then these are dependencies of the Adobe Flash plugin that are not being found on your system because they are not within the usual library paths.
P.S. If Firefox is working with Flash despite seemingly missing dependencies it is almost certainly because Flash itself depends on various Mozilla libraries and your distro has those libs installed within the Firefox directory only, rather than system wide. I have seen several of the smaller distros make this packaging mistake, meaning that Flash only works in Firefox/Seamonkey and not in any non-Gecko based browser.
For example, if libnss3.so was listed as not found but Firefox is able to load Flash look for libnss3.so within the Firefox directory:
$ find /usr/lib/firefox* -name "libnss3.so" -print
You can correct the issue in two ways. Either install the nss package if there is one or symlink the various missing libs from the Firefox directory into the main /usr/lib directory.