Yes, you can spread the ashes and till them into the garden , but after you do so, run a soil test.
However (!) , I would pull out the locust trees to use them elsewhere in the garden as poles, stakes, or fence posts.
They are remarkably impervious to rot, and depending on their diameter, should last several seasons.
Whereas Walnuts exude julgone as a natural herbicide to prevent competition, Locust trees increase the soil acidity to prevent undergrowth and plant competition.
Sparky1776 was right to apply the ashes around acidic loving plants (blueberries / azailaes/ Rhododendrons, etc. ).
That is why I would suggest a soil test after burning so as to determine soil akalinity/ acidity,
as well as determining what micronutrients amendments the soil might need to grow a successful garden.
Question: Do you happen to know if these locusts are Black locust , or Honey locust trees ?
Have you seen flowers on mature limbs?(locust trees are either male, or female). Locust tree honey is a prized light amber with a fragerant aroma, and will attract bees.
Generally , ashes will increase the pH of the soil, increase the avaliable calcium , but in large quantities also contributes salts (detrimental) in the soil.
That is why I suggest after the burn, to do a soil test. You and your garden would benefit from the soil test, anyway.
Thanks, TIK! I believe the trees were black locust.