i wouldn't call that a "map" seeing as alaska & hawaii are down where mexico's supposed to be & not even close to being the correct scale.
if you're after an image interface there are plenty of examples, google "flex image map".
if you really want to work w/spatial data have a look at
- ESRI https://developers.arcgis.com/flex/sample-code/using-samples.htm
- openscales http://openscales.org/
- modest maps Modest Maps | Home
- mapbox (for base maps) https://www.mapbox.com/
as i said, googling for "flex image map" turns up several.
no, ESRI & openscale APIs are free to develop. the map servers that you use may or may not be free. there are a few free map servers around, OpenStreetMap for instance.depending on your usage bing maps might also be free. the same applies to ESRI's arcGIS online.