I installed a program with Wine 1.5, but when I try to open it I get the following error
The program (A2J Author) is a program written in flash. Do I need to install Flash using Wine as well?
Yes, your program requires the Flash ActiveX (ocx) component, so you will have to install it within Wine as well.
In general, if a program running under Wine requires anything beyond the basic (built-in) Windows libraries, which are provided by Wine itself, you will need to download and install them separately under Wine. This includes Java, .NET, Flash, etc.