First off, you do not need a solar flare. However, you will need to make a few assumptions:
1) Continental Drift has ending. So long as continental drift exists the low points where the oceans fill will always be moving. However, this also means that volcanism will be largely ended, although a few minor spots might continue to exist for a time (think Hawaii, Yellowstone, and other spots where mantle plumes have caused volcanism well away from plate boundaries).
2) Now, simply presume that the lowest points of elevation are at the polls. Rain clouds will still form but away from these two oceans there will be little available rain to fall. I presume much of the rain falls around the 60-65 latitude, as occurs on earth, but it drains only poleward - perhaps drainage in other directions eventually fading away in the form of inland deltas which themselves suffer wet and dry seasons - think the orinoco (spelling?) in Africa, but further north.
One hard part will be keeping any moisture from the equator. It literally rains year round on an almost daily basis along the equator. Reducing available moisture will not completely remove this rain belt, as it will simply mean that the equator itself will likely be less arid than anywhere except near the polls. Think of it as the thorn scrub savanna - its 'rainy' season being barely enough to turn the grasses green for a month or two, and its dry season almost reducing the lands to a desert.
3) Another possibility is that the lands along the equator are mostly limestone. With the end of plate techtonics, this limestone will not move out of the way, so for a time any rain falling at the equator will carve out immense cavern systems - eventually to the point that whole rivers will exist underground. There are several places on this (real) world whose latitude, altitude, and prevailing rainfall would suggest should be quite well forested, but are in fact near-deserts due to the fact that all the water seeps underground - and stays underground for scores of miles, eventually coming up as aquafier springs, oasises, etc once they reach somewhat lower elevation lands where the land is no longer limestone. Perhaps just before you reach the polar oceans there are deltas, springs, oasises, etc in a band around them, as overland rivers from the poleward regions, underground rivers from the equatorward regions, etc come together, bringing greenery and life prior to meeting the actual oceans.
4) Lastly, for oceans to readily exist and be easily habitable by human civilization as is typically portrayed in games, the world will need to be much much warmer place. Just a few degrees warmer than earth - on average - will be enough to keep the oceans free of ice, but the temperatures will still be significantly low even in the summer - and let's not forget the few months of darkness each year. These are serious issues as far as potential growing seasons go. I think Anchorage, Alaska has a growing season of about a month - and it exists around 60N.
So these oceans should at least take up 30 degrees equator-ward from each pole (90 to 60 degrees) to reduce the amount of darkness per year along their coasts - and in the process allowing most of the rain in the 60-65 degree belt to fall back upon the oceans themselves. This could allow minimal middle ages style civilization as we think of it on the edges of the oceans. Raise the temperature a few degrees - globally - and we could probably increase the growing season at 55-60 degrees to perhaps 2 months ayear. At the 45-50 degrees, where the deltas, emerging underground rivers / aquifiers, and oasises perhaps exist, it might be as long as 3-4 months (maybe even 5 months, if the average world temperature is set high enough) - enough to create civilizations we might consider halfway normal for medieval time periods.
However, while civilizations could exist on the equator, it would be very minor - stone age most likley, and the distances one would have to travel - across deserts so vast as to dwarf anything on earth - would make meaningful trade between the poleward civilizations and the equator civilization (such as they are) virtually impossible. In effect, each pole would be totally separate from the other, as 7k+ miles would exist between them. This is the equivalent of crossing the Sahara Desert twice - west coast to Nile river, without any place to re-supply along the double length route. Even in modern times that would be difficult, especially as no roads would exist, no maps would exist to aid in determining the best route, and if any mistakes are made there is no place to re-supply in water or hunt for food.
Other Considerations:
Perhaps the underground cave systems have become multilayered over the millennia. So water still roars through the lowest layers, but the higher layers are 'dead' cave systems, dry, perhaps a bit unstable, but much cooler than the deserts above. These might allow for travel between the poles, as water could be re-supplied down below (perhaps eco systems exist in which to fish in these vast underground seas and rivers, allowing resupply of food as well as water?). Special caravan tribes might have memorized paths they take over the course of a year or two, moving south then north then south again, trading rare items only found from the distant poles only these caravan tribes can reach. They may need to exit the caves from time to time (cave ins block a path, or perhaps one cave ends and they must seek another to continue further south), so the complex route is not ready written down - presuming they would even consider sharing such sacred tribal knowledge with an outsider. Or perhaps there are several paths, and each time they choose the forks in the paths they choose based on the present circumstances.
Traveling this way cannot be fast. If we presume 5 miles a day (on average, sometimes faster, sometimes slower), it would take 3.5 - 4 years to travel from about 50N to 50S via such a route. Thus anything sold would likely be very expensive, and they would likely only focus on the items that could easily make such a long voyage and are less readily made (or not made at all) on the opposite polar civilization.
In any case, would this work for you? It's not quite a 'pole-only oceans world', as vast seas and rivers exists underground stretching from the equator to at least the 30-40 degree mark, if not as far as the 40-50 degree mark, and it presumes rivers stretch from the 60 degree mark to as far south as the 40-50 degree mark - and some of those flow not into the oceans but instead flow inland, form inland deltas, and dry out in their spreading. Does any of this work for you?