Kalki

The idea of yuga has  multiple meanings first one is this

When the king properly abides by the penal code following it to the letter, then that best of periods called the Krita Yuga sets in. Let this doubt not rise in your mind viz. whether the yuga is the cause of the king or the king the cause of the Yuga — know this for certain that the king is the cause of the Yuga. It is the king that creates the Krita, Treta or the Dvapara Yugas. Indeed it is the king that also causes the fourth yuga (Kali). The king that causes the Krita Yuga to set in enjoys heaven exceedingly. The king that causes the Treta Yuga to set in enjoys heaven but not exceedingly. For thus causing the Dvapara Yuga to set in a king enjoys heaven according to his due. The king however that causes the Kali Yuga to set in earns sin exceedingly. Thereupon that king of wicked deeds resides in hell for countless years. Udyoga Parva section cxxxii (132)

2nd one is the The end of the yuga cycle I. E the kali yuga where the Lord vishnu is believed to come . 

However the idea of kalki is only entertained by vaishnavas neither shaivas , shaktas or Ganapatyas (Ganesha worshippers) talk about it.

Avatar is expected to arrive at the end of the current Yuga — in 426,880 years. So we do not expect to be around  when kalki arrives.

Plus there are multi theories of yugas as well about kali yuga for example sadhguru jaggi vasudev and Swami Sri. Yukteswar (a self-realized master)  recalculated them and said that we are now already in the Dwapara Yuga.

If kalki wanted to arrive best time for him was during mughal rule or British rule..

Reason

During the period of invasion and plunder by the Ala ud Din Khilji's Muslim general Malik Kafur and his Delhi Sultanate forces in 1311, the Arabic texts of the period state that he raided a "golden temple" on river "Kanobari" (Kaveri), destroyed the temple and took the plunder with the golden icon of the deity to Delhi. According to Steven P. Hopkins, this is believed to be the Ranganathaswamy Temple.

severe second invasion of South India including Srirangam in 1323 AD.The sanctum's Vishnu image with its jewelry was pre-emptively removed by the Hindus before the Delhi Sultanate troops reached Srirangam by a group led by the Vaishnavite Acharaya Pillai Lokacharyar to Tirunelveli in Tamil Nadu. The Goddess Ranganayaki (Lakshmi) was also taken away to another location by a separate group. The temple was defended and according to the Tamil tradition some 13,000 Sri Vaishnavas devotees of Srirangam, died in the fierce.

It would have been better to the Lord if he had come at that time when his own devotees (vaishnavas) were been butchered mercilessly. 

He didn't come..
We don't even know wether we are in kali yuga or dwapara yuga

Now check the verse from vidura neeti (who was great devotee of krishna himself)

 
न देवा दण्डमादाय रक्षन्ति पशुपालवत् ।
यं तु रक्षितुमिच्छन्ति बुद्ध्या संविभजन्ति तम् ॥

na devA daNDamAdAya rakShanti pashupAlavat ।
yaM tu rakShitumichchhanti buddhyA saMvibhajanti tam ॥

"The Gods don't protect like a shepherd does with a stick.
To he whom They wish to protect, They give  intelligence."

- Vidura Niti, 3-40

na = not
devAH = gods, divine
daNDamAdAya = with stick (daNDa) in hand (AdAya)
rakShanti = protect (plural third person of verb rakSh)
pashupAlavat = like a cattle-grazer
pashu = animal
pAla = protect
-vat = like, when used as a suffix
pashu-pAl-vat = like a cowherd/shepherd

yaM = whom
tu = rather, instead
rakShitumichchhanti = desire (ichchhanti) to protect (rakShitum = for protecting)
buddhyA = with intelligence
saMvibhajanti = attach, join, (endow)
tam = that (person)

Similar thing
Lord Sri Krishna explains this in Bhagavad Gita in Chapter 10, from shloka 20 onwards:

The Blessed Lord said: Yes, I will tell you of My splendorous manifestations, but only of those which are prominent, O Arjuna, for My opulence is limitless.

Chapter 10, Verse 20.
I am the Self, O Gudakesa, seated in the hearts of all creatures. I am the beginning, the middle and the end of all beings.

Chapter 10, Verse 22.
Of the Vedas I am the Sama-veda; of the demigods I am Indra; of the senses I am the mind, and in living beings I am the living force [knowledge].

So instead waiting for kalki ( hero of the end times) we should focus on what we have now...!! 

We should follow the teachings of the Lord vishnu and try to neutralise any bad situation.
If the kalki comes.. Sure we will join his team, until then follow the above advices and do what is necessary.