Is it correct to pronounce sound /t/ in "to" as /d/?
0:54 And enclosed chamber has it opening beneath sea level, which allows water to float from the sea to the chamber and back. 1:03 (http://www.youtube.com/watch?v=gcStpg3i5V8 )

In the above video, the /t/ sound in "to float" is pronounced as /d/

So I saw the following video and found out that /t/ is often pronounced as /d/ flap t sound.
0:58-1:04 http://www.youtube.com/watch?v=0nwbzoIP14E
"The world 'to' will reduce to either the true T-schwa sound, or the flap T-schwa sound. "
She gives example "to the [tə ðə]/[də ðə]"

But is it correct to pronounce "to" as [də]?

Question

Is it correct to pronounce sound /t/ in "to" as /d/?
0:54 And enclosed chamber has it opening beneath sea level, which allows water to float from the sea to the chamber and back. 1:03 (http://www.youtube.com/watch?v=gcStpg3i5V8 )

In the above video, the /t/ sound in "to float" is pronounced as /d/

So I saw the following video and found out that /t/ is often pronounced as /d/ flap t sound. 
0:58-1:04 http://www.youtube.com/watch?v=0nwbzoIP14E 
"The world 'to' will reduce to either the true T-schwa sound, or the flap T-schwa sound. "
She gives example "to the [tə ðə]/[də ðə]"

But is it correct to pronounce "to" as [də]?

Answer

The "t flap" sound is similar to the korean syllable-initial "r" sound. The "t" in "to" is pronounced this way in US English when the previous word ends in a vowel or an "r." This is not the case in the main British dialects. This is how U.S. English is really spoken -- imitate how native speakers really speak, not how they think they speak. When your pronunciation is a close to reality as possible, your ability to understand the spoken word will be enormously enhanced.

Answer

...which allows water to FLOW… not float.

Rachel's videos are amazing, I'd follow whatever she says. Yeah, I guess it depends on the others sounds, it's something in between. I'd say go with the T sound. This is native speaker detail. Emulating this will not make you a better English speaker.

Answer

...the word is 'flow' not float.

Answer

The links you gave do not seem to work for me but I would say no, it is not correct - in your examples, the "t" should sound like a "t".

It may vary in different parts of the English-speaking world though - for example, I believe that in some parts of the USA, "duty" (which we in the UK would pronounce [ˈdjuːti]) and is pronounced [ˈduːti] in standard US English) can be pronounced [ˈduːdi] in some parts of the US.