Greetings from Northern Mi, Chipdasqrrl.
This is from www.sare/org.: Allelopathic
(naturally occurring herbicidal) compounds in oat roots and residue can hinder weed growth for a few weeks. These compounds also can slow germination or root growth of some subsequent crops, such as lettuce, cress, timothy, rice, wheat and peas. Minimize this effect by waiting three weeks after oat killing before seeding a susceptible crop, or by following with an alternate crop. Rotary hoeing or other pre-emerge mechanical weeding of solo-seeded oats can improve annual broadleaf control.
I think that your buckwheat planting following the oats will be fine.
For Rickey, I have one plot that is so sandy that I have called it beach. Last year, short version I planted Sudangrass and buckwheat in the field. I read that mowing sudangrass at 3-4 feet increases root development 5-8 times. Just what I wanted. Never had to mow as it only got about 1 foot high, somebody was nibbling some. I followed with winter wheat and was very pleased with spring growth. This year I planted sudangrass, buckwheat, timothy and Arvika peas (as a test on the peas). I hope that I get enough growth to have to mow. I guess that depends on the peas.