A couple of questions - do you want to grow Ohio Buckeye (Aesculus glabra) or Yellow Buckeye (Aesculus flava)? It's not really clear from your post but whichever it is you will want to make sure you get the right seed.
Secondly the fruit are nuts rather than acorns, which is the term for the seed of oak trees. I have not grown either of these but I have grown Aesculus hippocastanum (common horse chestnut). Basically you just need to gather fresh ripe nuts ('conkers') in the autumn and plant in a pot of any standard potting compost. Don't open the outer shell - wait until it splits naturally when the nuts are fully ripe and fall from the tree. After sowing leave them outdoors over the winter protected from rodents and most will sprout in the spring. Any seed you obtain now (in March) will be beginning to get stale but may be worth a try. In zone 5 I see no point in fiddling about with peat and fridges. It seems like an unneccessary extra step. I'd just sow them as soon as you get them and put them outdoors.

I don't know why your tree flowers but does not bear fruit. You might try posting this question on the Trees forum where there are some people who will be able to help you further.

Thanks Flora. The tree we have is the Yellow Buckeye. We seem to be the only ones around here with a Buckeye. I'll try your recommendations. There may have been some nuts, we have a few greedy squirrels here, and they might have beaten me to them. I'll have to get out there faster next year to try and get some. Marg

Marg - if you have squirrels it might be worth having a good hunt around for baby trees. They often 'plant' the nuts for you.