I don't think there is sufficient Biblical evidence to say that the Bible claims there was a worldwide flood.
If anything, it says there was a flood in the area where Noah was.
I'm not really aware of the evidence for/against this.
Here are genesis 6 and 7 with the important parts highlighted which prove that the bible claims that God made a world-wide flood.
Genesis 6
1And it came to pass, when men began to multiply on the face of the earth, and daughters were born unto them,
2That the sons of God saw the daughters of men that they were fair; and they took them wives of all which they chose.
3And the LORD said, My spirit shall not always strive with man, for that he also is flesh: yet his days shall be an hundred and twenty years.
4There were giants in the earth in those days; and also after that, when the sons of God came in unto the daughters of men, and they bare children to them, the same became mighty men which were of old, men of renown.
5And God saw that the wickedness of man was great in the earth, and that every imagination of the thoughts of his heart was only evil continually.
6And it repented the LORD that he had made man on the earth, and it grieved him at his heart.
7And the LORD said, I will destroy man whom I have created from the face of the earth; both man, and beast, and the creeping thing, and the fowls of the air; for it repenteth me that I have made them.
8But Noah found grace in the eyes of the LORD.
9These are the generations of Noah: Noah was a just man and perfect in his generations, and Noah walked with God.
10And Noah begat three sons, Shem, Ham, and Japheth.
11The earth also was corrupt before God, and the earth was filled with violence.
12And God looked upon the earth, and, behold, it was corrupt; for all flesh had corrupted his way upon the earth.
13And God said unto Noah, The end of all flesh is come before me; for the earth is filled with violence through them; and, behold, I will destroy them with the earth.
14Make thee an ark of gopher wood; rooms shalt thou make in the ark, and shalt pitch it within and without with pitch.
15And this is the fashion which thou shalt make it of: The length of the ark shall be three hundred cubits, the breadth of it fifty cubits, and the height of it thirty cubits.
16A window shalt thou make to the ark, and in a cubit shalt thou finish it above; and the door of the ark shalt thou set in the side thereof; with lower, second, and third stories shalt thou make it.
17And, behold, I, even I, do bring a flood of waters upon the earth, to destroy all flesh, wherein is the breath of life, from under heaven; and every thing that is in the earth shall die.
18But with thee will I establish my covenant; and thou shalt come into the ark, thou, and thy sons, and thy wife, and thy sons' wives with thee.
19And of every living thing of all flesh, two of every sort shalt thou bring into the ark, to keep them alive with thee; they shall be male and female.
20Of fowls after their kind, and of cattle after their kind, of every creeping thing of the earth after his kind, two of every sort shall come unto thee, to keep them alive.
21And take thou unto thee of all food that is eaten, and thou shalt gather it to thee; and it shall be for food for thee, and for them.
22Thus did Noah; according to all that God commanded him, so did he.
Genesis 7
1And the LORD said unto Noah, Come thou and all thy house into the ark; for thee have I seen righteous before me in this generation.
2Of every clean beast thou shalt take to thee by sevens, the male and his female: and of beasts that are not clean by two, the male and his female.
3Of fowls also of the air by sevens, the male and the female; to keep seed alive upon the face of all the earth.
4For yet seven days, and I will cause it to rain upon the earth forty days and forty nights; and every living substance that I have made will I destroy from off the face of the earth.
5And Noah did according unto all that the LORD commanded him.
6And Noah was six hundred years old when the flood of waters was upon the earth.
7And Noah went in, and his sons, and his wife, and his sons' wives with him, into the ark, because of the waters of the flood.
8Of clean beasts, and of beasts that are not clean, and of fowls, and of every thing that creepeth upon the earth,
9There went in two and two unto Noah into the ark, the male and the female, as God had commanded Noah.
10And it came to pass after seven days, that the waters of the flood were upon the earth.
11In the six hundredth year of Noah's life, in the second month, the seventeenth day of the month, the same day were all the fountains of the great deep broken up, and the windows of heaven were opened.
12And the rain was upon the earth forty days and forty nights.
13In the selfsame day entered Noah, and Shem, and Ham, and Japheth, the sons of Noah, and Noah's wife, and the three wives of his sons with them, into the ark;
14They, and every beast after his kind, and all the cattle after their kind, and every creeping thing that creepeth upon the earth after his kind, and every fowl after his kind, every bird of every sort.
15And they went in unto Noah into the ark, two and two of all flesh, wherein is the breath of life.
16And they that went in, went in male and female of all flesh, as God had commanded him: and the LORD shut him in.
17And the flood was forty days upon the earth; and the waters increased, and bare up the ark, and it was lift up above the earth.
18And the waters prevailed, and were increased greatly upon the earth; and the ark went upon the face of the waters.
19And the waters prevailed exceedingly upon the earth; and all the high hills, that were under the whole heaven, were covered.
20Fifteen cubits upward did the waters prevail; and the mountains were covered.
21And all flesh died that moved upon the earth, both of fowl, and of cattle, and of beast, and of every creeping thing that creepeth upon the earth, and every man:
22All in whose nostrils was the breath of life, of all that was in the dry land, died.
23And every living substance was destroyed which was upon the face of the ground, both man, and cattle, and the creeping things, and the fowl of the heaven; and they were destroyed from the earth: and Noah only remained alive, and they that were with him in the ark. 24And the waters prevailed upon the earth an hundred and fifty days.
Scripture teaches that we are dead in our sins, the death/destruction of wickedness while preserving godliness/righteousness would indeed be the breath of life from a religious standpoint. The same moral is seen when talking about Christ on the Cross; when you accept Christ you are suppose to die to yourself/your sins commonly referred to as dying on the Cross with Jesus, which is further expounded on in baptism ceremonies. Baptism symbolizes the death and Resurrection of Christ, in which the participant is supposed to die to themselves/sin and find the (everlasting) life in faith of God/Christ.
