IAG as a holding company could buy any airline they like whose shares are available for purchase. If they want to buy some obscure charter carrier, they can do so, but "can do" does not meant "want to"
IAG bought bmi as a way of increasing their Heathrow slots knowing they would have to lend a few out to competitors (Virgin and now Flybe)
IAG bought Aer Lingus because it was complimentary to BA. People who from the UK regions could then fly via Dublin to North America instead of Heathrow and IAG would increase their msrket power in the market between UK/Ireland and North America, their core market.
IAG are interested in Finnair because BA and Iberia are very weak on routes to Asia
I fully understand IAG can buy Flybe. BA Connect was substantially sold, IAG/Iberia do not own Air Nostrum, and the general outsourcing of regional flying in North America, how would Flybe complement the existing businesses owned by IAG ? Flybe is a UK-centric airline - how would it boost profitability of existing IAG-owned operations in the UK, namely BA, and thus why would IAG want to buy Flybe ?