I have a kindle fire hdx tablet and was wondering if I could download Adobe flash player on it.
There is no more Flash Player for Android and there won't be another. Android is no longer compatible with Flash Player since June 2012. Playing Flash content is very processor consumptive and it drains your battery, also shortening the life of it. Android (Google) recommends using either "Dolphin" or "Puffin" as your browser if you need to view Flash content with a mobile device running Android. They're both availabe in the GooglePlay store. These browsers use "server side" rendering to reduce the load on your device.