Every time the day hits the continent the winds would increase massively because water heats up way slower than soil/sand. I don't know how strong these winds exactly would be but you can expect a strong storm every 384 hours ravaging from the freshly heated up continental surface towards the dark and cold part of the continent which is still experiencing night.
So yes your storms would only be there at specific times when the day hits the continent again and another the other way when the day leaves the continent again because the surface of the continent will cool faster than the ocean and as such there will be a wind from the ocean towards the continent.
The mid days will probably be way to hot when not far enough from the equator. Also the nights will probably be to cold (without any source of heat) even at the equator.
Many plants could adapt to cycles where the open up in the sunlight and submerge them selves when the night hits to avoid getting ripped apart by the storm. After the storm they would probably resurface.
You said there are no mountain ranges to speak of but a thing which could happen as well is that behind hills in the wind shadow there will be a something like an oasis.
Because the storms would push all the soil in to the ocean except for hills and mountains as the storm cannot push through the hill soil will gobble up behind it and create something comparable to an oasis.
Because your day/night cycle is so long any civilizations will do one of two things depending on how your Continent is shaped:
- Your continent is completely reaches around the planet from east to west:
The things I said about storms do not come true as there is no sudden land mass that wasn't heated for a while and with out that there is no sudden temperature difference.
If the circumnavigation in possible far enough up north or far enough far south your civilization could be a large trek thats always walks with the beginning of the day or the end of it (in the middle it's very likely to hot) because in the night it would be to cold to be comfortable.
- Your continent does not reach around the planet from east to west:
The things i stated above about the storms and fauna become true and your civilization will probably live at the coast of the continent where the day comes by last.
Because one the storm (from a new day) will be the weakest there and when the night comes it will be the warmest near the ocean. During the day the civilization will look for shelter for the evening storm (when the day leaves the continent)
If your civilization has found a way to deal with the storm it could travel from the morning coast (where the day starts first on the continent) to the dawn coast and when the sun has faded they could travel back again. This of course depends on how far it is from one coast to the other if it is to far to complete it in less than 390 hours I would say the civilization would decide against this procedure.
Of course you could create a fast land animal which supports faster travel.