Question: How do Latter-day Saints reconcile scriptural accounts of the Flood of Noah with scientific evidence of continuous human habitation on the earth?

There is scientific evidence of diversity of species, language and of continuous human habitation

Modern scientific knowledge regarding the diversity of species, language and evidence of continuous human habitation does not support the Biblical story that a global flood wiped out most life as recently as 4,400 years ago.

The following criticisms are often applied and questions raised to Latter-day Saint (or traditional Christian beliefs) regarding the Flood:

It is claimed that LDS scriptures require Mormons to believe in a global flood, and that if LDS doctrine or leaders are fallible in their statements concerning the flood, then they must be wrong about other Church doctrines as well.
If Noah's Flood was not global, how do we account for Joseph Smith's claim that the Garden of Eden was located in Missouri?
Isn't it true that before the flood all the continents were all one land mass, since the Bible says that the earth was "divided in the days of Peleg."?

Many things about the Flood can be accepted regardless of belief concerning its nature

There are a number of basic teachings which many can accept regardless of the exact nature of the Flood :

There existed a prophet named Noah.
Noah was commanded by the Lord to construct an ark.
Noah warned the people of the impending deluge.
Noah, his family and the animals he collected were saved from the deluge.
The Lord made a covenant with Noah and his descendants.

Whether the Flood covered the entire earth at once, multiple smaller floods happened over a period of time, a localized flood happened, or no flood at all occured makes no difference

As demonstrated by D&C, a belief that this flood was global in nature is not a requirement for Latter-day Saints, we are encouraged to study and teach each other science to be better instructed in things pertaining to the Kingdom. Traditionally, many earlier members and leaders endorsed the global flood views common in society and Christendom generally. The accumulation of additional scientific information have led some to rethink their views as to the nature of the flood. Some still believe in a global flood. The absence of evidence for a global flood might mean that the Lord didn't want for that evidence to be present for discovery. Some believe in multiple floods happening over time, and some believe in a local flood — one localized to the immediate surroundings of Noah — is the best explanation of the evidence. Some believe there was no flood at all. People of different views can be members in good standing.

Latter-day Saint theology is not harmed by science

Doctrine and Covenants 88: 78-79

78 Teach ye diligently and my grace shall attend you, that you may be instructed more perfectly in theory, in principle, in doctrine, in the law of the gospel, in all things that pertain unto the kingdom of God, that are expedient for you to understand;
79 Of things both in heaven (cosmology, astrology, etc.) and in the earth (biology, geology), and under the earth (archaeology); things which have been (history), things which are (sociology, politics), things which must shortly come to pass; things which are at home, things which are abroad; the wars and the perplexities of the nations, and the judgments which are on the land; and a knowledge also of countries and of kingdoms--

When determining what God is trying to reveal, we shouldn’t be afraid of what science tells us about certain events recorded in the scriptures.

Eventually all will be revealed about the earth:

Doctrine and Covenants 101: 32-34

32 Yea, verily I say unto you, in that day when the Lord shall come, he shall reveal all things-- 33 Things which have passed, and hidden things which no man knew, things of the earth, by which it was made, and the purpose and the end thereof--
34 Things most precious, things that are above, and things that are beneath, things that are in the earth, and upon the earth, and in heaven

This seems to be a topic that we will learn more about and are learning more about “line upon line” (2nd Nephi 28:30; Isaiah 28:10) This shouldn’t pose a great threat to any part of our belief about science, scripture, prophethood, or the nature of revelation.

Notes

Question: How do Latter-day Saints reconcile scriptural accounts of the Flood of Noah with scientific evidence of continuous human habitation on the earth?