There isn't an instant loss rule for this. You keep shuffling until you get a Basic Pokemon and like you said, the opponent can choose how many cards they draw. If this is competitive play, the judge may give you a "Judge Ball" where they reveal cards from the top of your deck until a Basic Pokemon is drawn. That Pokemon is put into play and the rest of the cards are shuffled into the deck and then you draw six cards.
However, Talonflame is a gray area because even if you have Talonflame in your hand, you can choose to mulligan since it isn't a Basic Pokemon even if the condition to put it into your Active spot is met. You can have a deck with one Basic Pokemon and one Talonflame and can do what you said, assuming you draw Talonflame each time but I assume the judge would make you start with it after a few mulligan.