Are flowers / flowering plants vital to all life on Earth?
Angiosperms -- that is, flowering plants -- only evolved relatively recently on an evolutionary timescale, about 125 millions years ago. So for most of the history of life on earth there have been no flowering plants. Thus it seems highly likely that if angiosperms were to suddenly disappear, life on earth would continue. There might be a massive disruption of current terrestrial communities, but it's hard to imagine this resulting in total global extinction. In particular it seems unlikely that ocean communities would be undermined by the loss of flowering plants.