Why does F3 not work as Find Next in Chrome? I've already set up in system preferences, checkbox Use all F1, F2,... as standard function (checked on).

But still after  Cmd ⌘   F   on Chrome, pressing  F3   won't do anything... I expected Find Next would go.... only way is pressing  Cmd ⌘   G  

any chance?
F3, like the previous poster said, is a Windows convention.  Cmd+F is how all applications within OS X do a "Find".  However, you can re-map your Windows favorites to OS X with no problem.

If you want to make F3 = "Find Next" in Google Chrome, you can set that up yourself.

Go to [System Preferences] --> [Keyboard] --> [Shortcuts]



Select App Shortcuts and then click the "plus sign" to add a new one.  You will get a dialog box like the one below



Select your Application that you want to create the shortcut for, in this case Google Chrome.

Now, here is the most important part:  Type the name of the menu command exactly as you see it.  Go to the menu bar at the top of the screen and select the command from one of the menu drop downs.  In this case, it's "Find Next"



Enter that into your new Shortcut and assign the key you want, in this case F3.  It should look like this:



Click "Add" and you should see it show up as an new Shortcut.  Head over to Chrome and you will see that "Find Next" is now mapped to F3