I have taken a lot at times, up to 1-2g per day in powder form. I mix it with my tea, which also has theanine.
However I can't say it really helped with anxiety. TFA says some people claim its more effective than xanax. Maybe it works like that for some people, but not for me - it doesn't even put a dent in my anxiety - which can be pretty bad (struggling to leave the house). I've never taken xanax either, although my doc once gave me 10 pills of lorezepam for acute anxiety situations. Those basically had no effect on me too.
Theanine does reduce caffeine jitters although I usually only have that problem with coffee. These days I take 200mg most days mostly out of habit.