First check if Ohio and Kentucky share reciprocal rights on state line for hunting. Legally if the rights are shared you can hunt on any enbayments but not tributaries. You must hold a license of each state to hunt tributaries of the other state. This law is especially important during high water. You can only hunt the river at summer pool limits during high water conditions. Even when you hunt either side of the river of the state you hold a hunting license you cannot slide your boat onto shore. You must still have the boat floating unless you hold the out-of-state license. Even then there may be certain rules that now you are on land owner properties. Best bet is if you find a wonderful place to hunt along the river but is governed by the laws of the landowner owning into the edge of the river anchor yourself off shore and blind yourself up really well putting pockets of decoys on the inside and outside of your boat. Grab an old tree branch an lay it on your boat to look like a fall-out.
When it comes to tributaries if becomes even more specific on such things as navigable water. But there may be law changes that the land owner owns into the channel of the tributary and so forth. Check on this because laws have changed over the years.
Your best bet is to purchase the out of state license in Kentucky if you live in Ohio and vise-versa...If you do have both license even during high water you must not anchor your boat or decoy lines if not granted permission from the land owner.
If you decide to cross the river in-order to load the boat on a boat ramp in the opposite state you now are falling under the regulations of the state you load your boat. Be especially careful of this in-case season time frames are of different . A case I can give you for example is that Illinois had a season that started near 2 weeks ahead of Kentucky season. I would buy a IL license to hunt the first two weekends before Kentucky seasons. There are certain rules that you must follow when transporting game from state to state especially being very careful if seasons do not overlap. Similar to how you transport birds from Canada into the states. You have to tag the birds with your license number.
These stated laws pretty much hold true all along the Ohio river except up near West Virginia where hunting is not allowed on Sunday and then you can only hunt the legal state side you hold your license. Because WV is in the Atlantic Flyway and Ohio the central. Never took the boat that far east...
I have hunted the Ohio river from Indiana down through the mouth of the Mississippi River for near 20 years. My recommendations are still to get a guide for both states and also contact the local DNR of the state you are planning to hunt on the river. The State and Federal government when it comes to Waterfowl does not believe in ignorance. I honestly think you can get away with murder before hunting ducks out of season.
On some last notes be very careful no matter how many years you have hunted the river. It is very dangerous and is not prejudice of anybody. I do not know how the barge traffic is where you are but in Western Kentucky it is like driving a high way sometimes during the Holidays. Make sure you have a great spotlight and the proper navigable lights on your boat if leaving in the am hour or coming back in the pm. And no matter how well you think you know the river choose to sit at the ramp during Foggy conditions. I can remember several times during heavy migrations times that I have thought I was one place on the river and either the other side of the river, a barge dry docked waiting out the fog, and even Smithland dam proved me wrong. Though at trolling speeds it was dangerous conditions. I just barely escaped becoming a statistic. Lessons learned the hard way that became major changes in how I hunted the river. Not enough birds will fly anyway in these conditions. Also make sure you have all the equipment to necessary on your boat as stated in the boating guide lines. You just don't realize how often you need it when on the river especially when running and gunning. Also make sure you have an extra prop. No matter how many times you have followed a line on a GPS or just know that section of the river life proves you wrong with rip-rap, logs, cables, or other debris that was unexpected. My last advise is don't ever go on the river if you boat is under powered and never take you life vest off even when wading in what you think is shallow water. It is just not worth it.
Happy Hunting and Safe in your Pursuits..
Kristan