At the time I bought my Optimus One, I know that the phone is not flash-capable (though its platform at launch is Froyo already). But when I was doing a whimsical searches including “flash player LG Optimus One”, there is this thread at XDA forum that there is one compatible and designed for the chipset ARM11.
Here is the link: http://forum.xda-developers.com/showthread.php?t=1155071
1. Download and copy to sdcard.
2. Use a file manager and navigate to the apk, install it.
* Make sure to have "unknown sources" enabled on settings > applications.
* It won't work on Opera Mini.
* Only works with gingerbread (to be confirmed).
I've been told it works.
Sorry if it has been posted already or if it doesn't work in which cases I'll delete thread.