What does it mean when screen flashes blue?

The blue flash indicates that your "reaction time" - the slow-motion mode you can activate in melee combat - is recharged. This is mentioned on page 8 of the manual but not, if I recall correctly, anywhere in game.

As for the manual, there are scans available on ReplacementDocs, at least for the PS3 version; as far as I know, there's no official way to get the manual other than buying a hardcopy of the game. (Edit: @lunboks is better at searching than I am and provides a link to the official PC manual in the comments.)

When the screen flashes blue, it means your 'reaction time' is charged, allowing you to turn the level into slow-motion for a few seconds when you press a certain button (square of PlayStation, X for Xbox, and R for PC). Running will also recharge your reaction time They only briefly mention all this in the tutorial.

To get a manual I think the only way is to buy the actual packaged game disk (although they might have it on Steam. To check if it is there, right-click the game, click 'view store page' and then see if there is a 'view the manual' link in the lower right.