You should not have any problems while playing the games they run on Facebook using Mozilla Firefox or Google Chrome. May be you have some other problems on your computer or net connection.
You can do one thing, if your net connection is wireless or you have any other computers nearby then try your net connection on any other computer and see if even then, you have the problems.
If so your trouble is in the net connection or else on the PC. Besides you can try downloading the browsers again so if there are any problems in the browser it will be hopefully gone. And as an alternate you can use OPERA Or PROXY SERVER.
To download and install Opera Next 12, please watch this video
Well for me its Mozilla Firefox because its the most stable browser and as fast as goggle chrome,yes it does crash with adobe flash player,but there is some technique in order to avoid those crashes that happened on Firefox.
One of the thing that you should keep in mind is to make sure that you have the latest update for the adobe flash player or plug ins,you can check on the adobe flash player website if you have the latest version of the flash player or the plug ins.
If you don't have it yet you should download it on their website beside its free to download and just install this application that you need to play those flash games on FaceBook.