Of course you can; is there any problem when you try?
While the Flash Player Minimum System Requirements read:
what they don't take into account is the following:
1. A Core™ Duo is a 32 bit processor and has only two cores - nearly everything today is at least a quad-core
2. It's almost impossible to find a new computer without a 64 bit system, and it IS impossible to find a 32 bit Mac anymore.
3. A Corei5 (even a 1.6gHz) is a "hyperthreaded" processor, so it functions like a quad core, and that means you have a "root mean" processor speed of 6.4gHz with your MacBookAir - well over the 1.83gHz required as a minimum.
Use the offline installer Flash Player 12 (Mac OS X) to install from and you'll be just fine.