I have a xbox 360 console with 4gb drive. A game that I wanted to buy is not available locally, but I can buy it at the xbox marketplace and download the game. The download size is 3.9 gb. Can I download the game and install it on the flash drive and then play the game from the flash drive?
It's possible. From personal experience, I have a 16 GB flash drive that I use for my 20 GB Xbox. I formatted it, and downloaded some games onto it (like Fable 3 and The Orange Box).
There's more info on Microsoft's support site.
If it is an XBLA game, you should not experience any issues running it from a flash drive. I had burnt out my hard drive at one point, and could only run games off of flash drives. The one snag here is that games that come with discs need the disc in the drive regardless of having had installed them or not.
Now I would assume that is not the case if you purchase the game through the marketplace. Say you purchased halo 3 and downloaded it, I would figure that Microsoft has made it such that, that version, does not require a disc to play. Thus it should run from where ever it is, be it hard disc drive, flash card, or external hard drive.
When you originally download the game make sure to set the flash drive as its destination. But really I cannot foresee any issues with the game running on the drive. As the important elements of the game are loaded into the machines RAM and then played.
Yes, you can definitely play a full 3.9 GB game from a thumb drive.
I recently purchased a full game (Games on Demand) online, which auto-downloaded when my Xbox turned on. I didn't know it at the time, but my internal hard drive was filled, so the download defaulted to my already-formatted and plugged-in USB thumb drive. The game played fine from there. (Official confirmation, via LOL. NO.)