How to turn on flyspell mode with AUCTeX?

Try (add-hook 'LaTeX-mode-hook '(flyspell-mode t))

This will force flyspell-mode to turn on, instead of toggling it.

(add-hook 'LaTeX-mode-hook '(flyspell-mode t))

I would be surprised if the above worked.

The following works (using emacs 24):

(add-hook 'LaTeX-mode-hook #'turn-on-flyspell)