Well given recent developments (i.e. Flash no longer existing on Android or at least not for much longer) and the fact that Flash will be totally discontinued in probably less than a year, it's a pretty sure bet that Flash is your worst option.
Flowplayer I have never heard of in itself but given that it is advertised as a "Flash video player for the web", it comes with all the same issues.
Sliverlight has largely failed to take off in pure video as a rival to Flash given it's significant limitation to only really IE.
So ultimately it comes down to three options (two of which you haven't considered - one is a hybrid). You can either use HTML5, or go the popular YouTube way. Adv/disadv of both:
YouTube: Make videos private so not searchable if wanted, will play on any device due to Google's massive effort to get YouTube working in all browsers (will do it all for you), Buuut videos will be easier to download.
HTML5: The up and coming best way to embed videos. Still easily downloadable but will work in almost all browsers (use correct video format - see W3Schools) and will be a low maintenance method.
(Note to your client: If they can download it to view it in browser, they can easily download it and save it to their hard disk. No way around it at the moment unless you get into messy DRM stuff which isn't actually (other than Flash) supported on the web yet. Hopefully future versions of HTML5 will introduce some combination of HTTPS/DRM for the video/audio tags but at the moment it's not possible. You will just have to put up with people downloading it - it's why people are so riled about copyright/intellectual property/file sharing sites especially with movies at the moment - see the news.)
I am assuming given your client's market that XP/IE8 must still be supported (which is sensible and fair enough). This does leave you with a third and final option that I can think of and one that I highly recommend (based around Google's approach). I will assume, form your own description, that you are competent enough to implement this theory by yourself:
1) Upon receiving a request, grab the User Agent
2) If the User Agent matches the IE8 User Agent, continue to step 3, else step 4
3) Output into your HTML a Flash embed tag for the video. Go to step 5.
4) Output into your HTML an HTML5 Video tag for the video. Go to step 5.
5) Continue page as normal.
This will allow you to use maintainable/reliable up-to-date methods (i.e. HTML5) while still having a graceful degradation to XP/IE8. I have no doubt that Flash will remain available for XP users for some time - long enough at least to last with IE8 - even if it is not "officially" available from Adobe.
Hope this helps,
HTML5 - Setting multiple possible video sources to support all browsers - using different video types for Safari and IE.
A very good page from W3Schools covering all encompassing HTML solutions and the YouTube solution - read the full page!