Your young trees look great. It is a difficult task to get those nuts to sprout, so I congratulate your success.

Some information I read  would suggest you keep this young sprout in a container until a year's growth so it can be protected from chipmunks, mice and rabbit damage. They will make great efforts to find and eat your seeds and young foliage. 

Definitely keep in mind when selecting a site that a Ohio buckeye tree can grow 40-60 feet tall, so if you are permanently planting  select a well drained site with good drainage and sun to partial shade.  They need to be moist, but not too wet.

1. PLANT SEEDLINGS AT LEAST 6 INCHES APART. Buckeye  seedlings should get at least 12 inches tall the first year at a spacing of 6 inches or more. Transplant seedlings when they are dormant, preferably in the spring. The photo looks like they are already out of dormancy, so you might want to wait to plant in the ground.
2. To plant, dig a hole slightly larger than the root ball.  Carefully place the root ball in the hole and fill around the roots with loose soil. Make sure the roots are spread out and the ends of the roots point down as loose soil is backfilled into the hole. Plant the trees slightly deeper (about 1 inch) than they were in the pot.  After planting, water the trees well to settle the soil around the root system. Mulch around the trees to conserve water. The trees should not be pruned at planting time.
3. Fall and winter planted trees should not be fertilized at planting time unless you use a slow release fertilizer tablet or packet. Trees should be fertilized in the spring after they start growing. Use a liquid fertilizer or granular fertilizer. Control weeds and grass around the trees, and make sure the trees have adequate moisture during the first growing season. Do not over-water the trees: thoroughly wet the soil once per week to once per two weeks if they don’t receive adequate rainfall.  These are a few of the Ohio state fact sheets I found regarding the Ohio Buckeye. Good Luck!
4. https://plants.usda.gov/plantguide/pdf/pg_aegl.pdf
5. https://insights.osu.edu/food/growing-buckeye-trees
6. https://advancement.cfaes.ohio-state.edu/node/3804