You are not alone. As ESRI stops supporting both Silverlight and Flex, hundreds of organizations will need code converted.
Some of the risks involve limited JS API functionality. One simple yet unsolved issue we faced was map rotation. While Silverlight supports this, the JS API does not. Our customers are use to seeing their maps rotated by 243 degrees. Not allowing map rotation would really reduce customer ratings and cause confusion.
The most efficient way would be to continue using your current Flex app, while you dive into recreating existing widgets and tools in JS. I wouldn't imagine you would lose much of your widgets as they are probably more backend geoprocessing services, however some of your front end functionality may change. Stay in close contact with ESRI Programming Support Analysts and GeoNet.