Some good flash games to play online are Jacksmith, Rogue Soul and Super Mario 63. These are all free games that only require flash capabilities.
In Jacksmith, the player is in charge of making weapons for their warriors. They need to traverse the rough land to find items to make shields, bows and arrows, and swords. Battling is also a part of the game once all the warriors have their weapons.
Rogue Soul is a game where the player goes through a side-scrolling type of adventure. They need to be fast while dodging, jumping, running and sliding through the different levels. Super Mario 63 is a manmade flash game based on the popular Super Mario franchise.