Does this Digital output design correct?

[Yansi]

That is the absolute max ratings, not recommended operation voltages.

ULN2803 is supposed to work with 5V (and likely 3V) logic, for higher voltages (CMOS) there was the ULN2804.

[MarkF]

And the ULN200x series as a comparison with the same max specifications:

[Danesh_SA]

VN340 and BD8LB600FS  are great options but the price tag is HIGH!
I think for lower price tag we have other options such as:
1-TI DRV8803 is an inductive load switch with integrated protection ,
3-TBD62783 is 8channel source type DMOS transistor array WITHOUT BUILT IN PROTECTION(Lower power consumption and better operation )
4-discrete MOSFET or BJT drive

But still I don't understand WHY ITS NOT GOOD TO USE DISCRETE FLYBACK
DIODE WITH EACH ULN2803 OUTPUT,COULD SOMEONE EXPLAIN IT IN DETAILED?

[Yansi]

Using a motor driver as an output switch, is dumb idea, as its over-current protections rely upon the load having at least a bit of inductance. Will likely burn to shits when shorted directly. Also, you have a totem pole drivers there.

Price tag high and bla bla...  Then find another solution with the same robustness, as the industrial/automotive drivers have.

Not sure what you want it to use for, but ULN2803 is not the recommended way for any kind of a slightly industrial application, let alone one when user can access the outputs. Remember that fuses are fire protections, not for silicon protection. Transistors always burn faster than fuses!

But still I don't understand WHY ITS NOT GOOD TO USE DISCRETE FLYBACK
DIODE WITH EACH ULN2803 OUTPUT,COULD SOMEONE EXPLAIN IT IN DETAILED?

Because there is no need for them, the internal ones shall be absolutely fine. That's why they are there.

Also, if you look further without fussing about the price tag being high, you can sure find solutions like BTS3118D, etc. There is a metric crap ton of these cheap single channel ones, if you just bother to look.

Problem only is, if you want the output for a PWM operation - most of these protected switches have very slow turn on and off.