In reply to defaid:
Hmm. no edit button. I guess I left it too late.
I've a suspicion the acid/bicarb mixture was originally intended to be used as a paste, for rubbing or scrubbing, with the acid doing the work, the bicarb acting as a mild abrasive and the evolved CO2 serving to lift dirt off the surface.
I doubt that a very watery solution would do much. You'd probably get as good a result using just vinegar or lemon juice. On the other hand, if you have a bottle brush, you could mix up the paste and use it with the brush for scrubbing the inside of the flask though, to be honest, nowadays you'd probably get the flask just as clean with a dash of Fairy.
D