I just downloaded a MySearch app in Google Chrome and it says it can access all the data on my computer. Should I be concerned?

You need not be. This is standard language from Chrome applied to extensions. You can read more about these warnings here.

MySearch apps (GameOn, MuzikFury and SeenOnScreen) do not look at any data on your computer other than the files they install to enable the products on your device. The apps do not collect personal information of any kind, nor do they monitor or report any of your browsing activity. In short, the goal of the apps is to provide a superior search experience on an anonymous basis and without any additional monitoring, contextual ads or other nuisances.