Confirming DC circuit configuration
Can experts in this field confirm that the circuit will work safely?
(without voltage spike, etc.)

If all you have is a block diagram then no, hardly anything can be confirmed or denied. You need to supply a schematic and that will be the first point of reference to evaluate if there is likelihood of excessive EMI.
I say EMI because voltage spikes are quite often necessary features in circuits and, when you are driving motors and trying to use regenerative braking, you will naturally see what I can only superficially describe as voltage spikes.

Also, do I need a flyback diode with the motor or any of the relay for
the induction spike?

If all you have is a block diagram then no, hardly anything can be confirmed or denied. You need to supply a schematic and that will be the first point of reference to evaluate if there is a need for a flyback diode for motors or diodes.
Quite possibly the answer is yes but without a schematic that's impossible to tell.
Moving on, once the schematic is analysed you will need to make a printed circuit board and part 2 of this question (same questions) involves looking at the PCB layout to see if there are any improvements that can be made but, without a PCB layout this is impossible.
It's not even worth a guess.
One guess - I suspect you might have meant buck converter for the lower boost converter (just a feeling in my water). And, I also suspect that relay contact 4 should be on the output of that converter and not the input: -

So, in some respects you can analyse a block diagram to see that the general idea makes sense and, even if my above modification is incorrect, at least it might provoke thoughts about what is actually needed and may uncover other areas that need more thought before a schematic is drawn.