Can someone explain the meaning of 都 in 我都說?
The speaker you're referring to has these subtitles following his speech: 


  所以说真的, 我们每次学的时候, 难怪我都觉得说, 人家看我怪怪的。 我都说(something in Japanese),
  可是那个(something in Japanese)是女生的, 对不对？


What I'm actually hearing (I've double checked with speed 0.25) is this: 


  所以说真的, 我每次学的时候, 难怪我都觉得人家看我的时候怪怪。 我都说(something in Japanese),
  可是那个(something in Japanese)是女生的, 对不对？


He speaks at a fast pace, which results in being not completely 标准 (standard), similar to English natives saying 'wanna' instead of want to. 

What I hear might also be different from what he actually says, please correct me if I'm wrong.



Answer to your question:

The 都 in '我都说' (which is your question), means 'always'. The speaker doesn't say 每次, but that is exactly what he means. See here for expressing 'always' with 每次...都.



In addition to this, I would like to add to the answer of songyuanyao (I don't have enough reputation to comment).

都 means already, only in the structure: 都...了. See here for further explanation.