Flex: How to add a tab close button for TabNavigator component

I've got a project with styled tabs (I assume you mean the tabs themselves, and not the content). I'm sure there's other ways, but this is what I seem to have ended up with:

.myTabStyle {
    tabStyleName: "myTabs"
}
.myTabs {
    backgroundColor: #ff0000;
    fillColor: #000000;  /* this is the tab widget itself, not the content */
}
<mx:TabNavigator ... styleName="myTabStyle" .. >

There's several places in Flex where you have to use CSS styles to refer to other styles to drill into the widget you want (another example is setting the titlebar style on a TitleWindow).

I hope this helps.

By the way, I've seen occasional "tearing" on Mac & Windows, FireFox, IE, Safari, Flash 9 and 10 with large fonts & colored tabs--I'm not sure if this something I'm doing, something about the larger fonts, or the colored tabs themselves--but just a heads-up. This only happens when building with the Flex 3 SDK (never saw it with Flex 2).

You can do this by making use of TabNavigator's getTabAt() method which returns the Button that makes up the visual tab. You can then set that Button's visible property. It's a little tricky to get this setup with a bindings, but it's doable.

You could also consider just disabling the tab instead, which you can do by setting enabled on the corresponding TabNavigator child (for which visible didn't work).