Samsung ships a customized version of Flash with the Galaxy Tab that is incompatible with the tablet. However, there is a solution to it. Ageitgey at xda-devs has come up with a solution that I would not recommend to the casual users as it requires hex-editing, something not recommend for the weak-hearted blokes, but the end result is tasty.
Here is how to do it (copy-n-pasted from this post):
1. Make sure your Galaxy Tab is rooted. If it isn’t, you can easily root it by downloading z4root from the Android Market and running it.
2. Make sure you have Root Explorer installed. You can buy it for a few bucks in the Market if you don’t already have it. It’s a great program and worth the few dollars.
3. First, you need to get rid of the pre-installed version of Flash that comes with the Tab. Using Root Explorer, move install_adobe_flash.apk from /system/app/ to /sdcard/. You want to make sure it no longer exists in /system/app/ but that you have a backup copy in /sdcard/.
If you are like me and already deleted the original install_adobe_flash.apk from the Tab without backing it up, you will have to grab a new copy from a Galaxy Tab ROM. Find a Galaxy Tab ROM online (P1000XXJK5 works), uncompress it, mount factoryfs.rfs as an ISO, and get a new copy of the apk file out of it.
4. Next, you need to hex edit this version of Flash to make it appear as though it was Flash for Windows.
Now that you have install_adobe_flash.apk in the /sdcard folder, plug in the tab and enable USB file sharing.
Copy the apk file to your computer and unzip it. Inside, you will find /lib/armeabi-v7a/libflashplayer.so.
Open libflashplayer.so file in your favorite hex editor (Hex Fiend is good on OSX). Search for the ascii string "AND 10,1,92,8" (the numbers might be slightly different depending on your Tab’s ROM). Replace that string with "WIN 10,1,102,64". Make sure the hex editor is in overwrite mode when you do this. The new string is longer than the old string, but you don’t want to change the file size. Save the file.
5. Now you need to get your hacked version of Flash back onto the Tab.
You have a few options. You could install the flash apk using "adb install install_adobe_flash.apk". That would get you flash back. Then you could copy your hex edited libflashplayer.so to the /sdcard folder and then use Root Explorer to replace /data/data/com.adobe.flashplayer/lib/libflashplayer.so with your version. That will work fine, but you will have to recopy your modified libflashplayer.so over the original one every time you reboot.
The better option would be to rebuild install_adobe_flash.apk with your hacked library included. Then you can install your modified flash apk.
6. Browser Settings
Dolphin HD is the best choice. You need to make sure the user agent is set to "Desktop". It seems like you also need Flash set to "Always On", not "On Demand". It seems to act flakey with On Demand but your experience might vary.
Did it work for you? Let me know!