It can be easy to think that you are too old to play flash games. There is no reason to think this though.
Although the games are kept up to date with their content and have something to appeal to younger players, there are games to suit all ages.
Whether you like retro style games, puzzle games, driving games or something else, you will find that there are so many games to choose from. You will be more than likely to find something that you enjoy playing and you have nothing to lose by looking and trying some out, because they are all free.
Many games are not written with a certain age group in mind and so you should find that you will find games that you like (you should Sift Heads for sure or tank games). Some might be aimed at children and others at teenagers, but most games publishers do not want to eliminate a lot of their potential audience by aiming at a particular age group. You should therefore find that when looking at the games that are available, you will find a lot of things that you like.
It can be a good idea to consider what sorts of games you like and search for those types. You will then be able to find out what is available for you to play and you will know whether there are many games out there that you are likely to enjoy. Look for the genre of games that the ones you like fit in to as well as the specific game and then you will be more likely to discover new games that you are likely to enjoy.
It is well worth being confident and searching for games even if you think that you are too old to enjoy them. Until you look, you will have no idea whether there is something out there that you will enjoy. It is worth hunting round as you could find that you will discover some great games and perhaps even find a new favourite. Games are written for all ages and you never know what you might find, that will suit you. You may even find some games that you had no idea that you would enjoy, so why not play something new and see whether you like it. You could be pleasantly surprised.