Yes, students with open degrees from KKHSOU and IGNOU are eligible to apply for UPSC and APSC Civil Service Examinations. The eligibility criteria mentioned by UPSC and APSC Civil Service examinations is that aspirants should have completed their degree from a UGC-recognized university.
KKHSOU and IGNOU are UGC recognized. So, you are eligible to apply.
You are eligible for both UPSC and state PCS examinations just like any other university. Your degree is also equivalent to a degree from any other university. In fact, some of the IGNOU students have also cracked the UPSC exam with good ranks.
So, just like him, you can also make your entry in the list of toppers not matter from what university you are. All the best!