According to http://hypertextbook.com/facts/2001/SyedQadri.shtml, the total volume of the world's oceans is 1.3 to 1.5 billion cubic kilometers, which comes out to 310 to 360 million cubic miles. The surface area of the Earth is about 200 million square miles. So if the Earth was a perfect sphere, with no mountains, no valleys, no ocean trenches, the water would cover the surface about 1.7 miles deep.
There's water in the ice caps, underground, and in the atmosphere. Perhaps all this water was on the surface during the Flood. But by most calculations this is a relatively small percentage -- hydrologic scientists generally say that 97% of the world's water is in the oceans, 2% in the ice caps, 1% underground, and lakes a rivers a tiny fraction of 1%. So unless there's some very large unknown water reserve -- underground, I suppose -- adding these things in wouldn't change the 1.7 miles much.
Of course the world does have mountains and valleys, so some places are above the water level and others below. The highest mountain is of course Mt Everest, which is 6 miles high. The lowest point is the Marianas trench, 7 miles deep.
So the most obvious scenario for a Flood to cover the whole world is that the mountains before the Flood were smaller than today and the trenches not as deep. If the highest mountains were 1/4 the height today, then they would all be covered by water.
Creation theorists generally suggest that the Flood caused major geological upheavals including relatively rapid movement of the Eartth's tectonics plates, resulting in mountain formation. That is, they say that the high mountains in the world today were formed during the Flood. Of course for the world to not be covered in water before the Flood, the amount of water in the oceans would have had to have been smaller. Genesis mentions water coming from both rain and "the fountains of the deep". The theory generally calls for more water vapor in the air in the form of a large vapor canopy, and also more water underground.
So ther's plenty of water if only the Earth was more nearly spherical before the Flood.