Nope. No way having the child walk 1 block to the car.
And, what will you do when there is bad weather? Still have him walk 1 block?
Now, MANY families have this sort of schedule.
2 or more kids, different schools/grade levels... and they do it.
How?
They tell the school.
They tell the Teacher.
The child then waits in the school office, to be picked up.
No problem.
Now, for the Kindergarten child... isn't it going to be full-days at some point? Not just in the afternoons?
Next: DO NOT WORRY, about the preschooler "missing" his sibling. It is NO big deal! The preschooler will probably be very tired/nap after he comes home after preschool, anyway.
This is NOT a factor, in planning/deciding when to send your kids to school.
LOTS of Moms... are waiting at schools in order to pick up their other kids... WITH their other baby/kids in tow, waiting in the car too. It is fine. I did that too when my son was a baby. It works. You simply drive to the school early to get parking...and wait. With your 2 kids. You bring drinks and snacks. Get out and walk around. It is really no big deal.