The epics Ramayana and Mahabharata happened in Treta yuga and Dwapara yuga respectively. Likewise, is there any epic which will take place in Kali yuga?
The episode of Kalki avatar of this 28th Chaturyuga cycle is not written anywhere, as it is not yet recorded in the Causal Ocean/Ocean of Events. It is Vishnu's Will and His Will only. Gods can know humans' wish and will, and can write down an entire story for what humans can do in the year 2110 AD. But knowing Vishnu's wish and will in the future is beyond their reach. So Kalki, who's not appeared yet is not recorded anywhere except the facts which were predetermined, like He will be born in Shambhala, will receive celestial weapons from Parashurama, will be assisted by Hanuman, etc.
Are you talking of Lords Appearance in this world in Kali Yuga? Then the answer is Yes. Sri Chaitnya MahaPrabhu appeared in Bengal around 500 years ago. The entire episode is elaborately described in the epics, if you like to call it that way, Chaitanya Charitamrita, Chaitanya Bhagavata and Chaitanya Mangala
He appearied especially to deliver the people of this age.
Well, this is a very broad question. I can only say epics do not happen because they have to happen. Great sages from ancient times written those great works to mention coming generations about how they need to lead life and what happened to various people who obeyed or disobeyed god and dharma. These epics are serving the sole purpose of enlighting the generations. Kaliyuga is the last part of the Mahayuga (which contains kruthayuga, threthayuga, dwaparayuga, kaliyuga) and after kaliyuga the clock resets to kruthayuga where these dharmas are no longer valid and have more stricter rules.
Anlayzing those epics what scholars conclude is in kruthayuga the god and bad are separated by planets. Gods recided in urdhva lokas and demons in adho lokas, and whenever there are problems, god took incarnation of some form and killed those demons. In threthayuga, good and bad were in the same world and separated by kingdoms (Rama and Ravana). God just not changed his form, but rather took birth, and he not only killed ravana but also showed the world how one should lead life to attain higher world and ultimately moksha. In dwaparayuga, good and bad were in the same family (Kauravas and Pandavas), then god motivated good people, corrected them, and made them kill the bad ones. He did not do it by himself.
In kaliyuga good and bad are in the same person, no one is perfectly good or bad. So in kaliyuga people do not change much by teachings or preachings or even model living, and people tend to become more bad as the kaliyuga progresses. Hence the only way to correct is by creating maha pralaya (destruction as kalki).
Kalki is the Avatar of Kaliyuga. Though Lord Venkateswara is born to fulfill some of the promises he made in previous incarnations but he didnt kill any evil.
Logically Kalki will fight with Kali who is the head of Lust, gold etc.. currently kali is not visible to the physical world. so Kalki will be too.
Kalki will fight with Kali in a different dimension i guess.
Why im saying like this is, in previous incarnations does asuras physically exist in the world and people were able to see the vishu avatar physically. Now Kali born before end of Dwapar and he does still exist but we cannot see him.