Adobe has released a new Flash Player 10.3 build in the Android Market, strangely if you visit the page from desktop it still shows the version 10.3.186.3 while if you visit from your Android device, the latest Flash Player for Android is with build number 10.3.186.6, updated on 25 August, 2011. Maybe they are still updating at the time of writing, but you can download it right now.
Download Flash Player 10.3 for Android Phone and Tablets
Market Download link, if this link still shows version 10.3.186.3, visit the link directly from your Android Phone or Tablet.
Flash Player apk file size: 4.23MB