The note A# in your transcription is a Bb and the key the song that you’ve copied is written is Bb (respectively G Aeolian, I‘ve edited as the final note is G).
If you don‘t play with another instrument like piano or guitar it doesn‘t matter in which key you are playing and you don‘t have to mind the tuning of your instrument.
But I think you‘d better play it in F than in Bb, as the fingerings for the b-flats are sometimes harder to learn. As you‘ll play in F it will sound in G and C-instruments will have to accompany in G. (Your D-flute is transposing a whole tone up).
The following notation is in F, when you play it as written your flute will transpose it to G. It starts with CAA (corresponding to yours @ 2:59)
(If you want to play to a video that is in Bb then you had to play transpose a whole tone down - that means in Ab - but it will be easier to find a version that you can transpose into another key.)
If I can give you an advicie: It would be better to learn reading sheet music instead of playing just from letters - as your example - or fingerings like this:
This would be more helpful and beneficial for the future.