So the basics:
1) Affinity want out
2) Virgin don't have the cash to buy the Affinity stake
3) Virgin are obviously interested in where it goes
4) If Virgin do sell some of their stake, most likely they will maintain a controlling interest
Virgin Australia do have they money, in their last reporting they had just over $1 billion of cash in the bank. If they want to spend it to buy out Affinity is the question. As per some comments buying it would be a luxury, but as Velocity is a profitable business it may make a lot of sense.