Is it possible for each of those who committed fornication to flog the other a hundred lashes to purify the sin, or what is the solution for repentance without disclosing the matter, and how is the flogging carried out if it is possible?

You must conceal what major sins you have committed and suffice with repenting to Allah and regretting what has transpired from you. Similarly, the individuals you mentioned must repent to Allah, regret their actions, and conceal their sins. For the corporal punishments (Hudud) are carried out by the ruler based on the person's confession or the existence of evidence, and that is for the purpose of concealing the Muslims. Conceal yourselves where Allah has concealed you, and sincerely repent, for Allah loves those who repent and accepts repentance. The Messenger of Allah, peace and blessings be upon him, said: "O people: Avoid these abominations that Allah has forbidden you. And whoever commits any of them, let him conceal himself." Thus, concealment, repentance, and regret are more fitting than confession.