According to this question it is possible to hide fmx taskbar icon by changing window style to WS_EX_TOOLWINDOW. In XE2 and XE3 this code works:
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Just tried this in XE7 and of course it didn't work. However a little look into FMX.PlatformWin shows the application handle is now exposed through the ApplicationHWND function, so the code that works on XE7 (don't forget to include unit FMX.Platform.Win and Winapi.Windows) is...
procedure HideAppOnTaskbar (AMainForm : TForm);
var
AppHandle : HWND;
begin
AppHandle := ApplicationHWND;
ShowWindow(AppHandle, SW_HIDE);
SetWindowLong(AppHandle, GWL_EXSTYLE, GetWindowLong(AppHandle, GWL_EXSTYLE) and (not WS_EX_APPWINDOW) or WS_EX_TOOLWINDOW);
//ShowWindow(AppHandle, SW_SHOW);
end;
The ShowWindow at the end is optional - it seems to make no difference. You can remove the extended styles and restore the WS_EX_APPWINDOW style to show the toolbar icon again.