Doesn't look like this will be streamed legally. Perhaps check TSN Go.
If you are in the US, this will be broadcasted on NBCSN.
The League has clarified what happens if NJ wins the lottery:
Quote:
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To ensure that the odds of all 13 Clubs eligible to win the Draft Lottery are enhanced equally to reflect the Devils' situation, the Draft Lottery this year is being modified as follows: the Devils will still be included in the Draft Lottery drawing on the same basis and with the same odds that would have normally been assigned to the Club based on and consistent with its regular-season finish. However, in the event the Devils win the Draft Lottery, an immediate re draw will be conducted to select a different recipient of the first overall selection in the First Round. The same process will be conducted as many times as necessary to ensure that the first overall selection is awarded to a team other than New Jersey. The Devils will be entitled to the 30th selection overall in the 2014 NHL Draft (the last pick in the First Round). The Devils are not permitted to trade or transfer their right to the 30th overall selection.
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From the Flames POV these are the possible outcomes:
1st overall 10.7%
4th overall 58.0%
5th overall 31.3%