Is this flapping?

https://youglish.com/getcid/19629243/Wouldn't/us

I realized that I make a flapping sound [ɾ] when I pronounce "wouldn't".

But I also realized that not every native speaker does that.

Then I found this clip, which I think is flapping like my pronunciation.

So question : Is that woman in the clip doing flapping? And is it okay to do flapping with words like "wouldn't" , "couldn't", or "didn't"?

It's hard to be sure, but I think you're right. She's saying a flap followed by schwa: [ɾən]. Many (including me) say [d] followed by syllabic [n] here. The reason you don't get a flap followed immediately by syllabic [n] with no intervening vowel is that the flap articulation requires the tongue tip to touch the alveolar ridge only briefly, but the tip can't leave the ridge immediately if [n] follows; the [n] requires tongue tip contact.

I have a good friend who says "wouldn't" with flap and schwa, and he is from California's Central Valley. (He also has a flap in "button", which is lots easier to hear, because it doesn't sound at all like the glottal stop that most have here.)

No, she is using [d], not [ɾ], because you can hear a brief friction ([z]-like sound) after /d/, which doesn't occur with [ɾ]. But she is pronouncing the 'n part as [ən], not [n̩] like many other people do. [ən] and [n̩] are interchangeable in this position (see this Wikipedia section for more).

As for your last question, yes. In North American English, /d(ə)n/ preceded by a vowel as in wouldn't, couldn't, didn't, etc. can be pronounced [dn̩], [dən], or [ɾən]. My impression is that [dn̩] (with a nasal release) is most common, followed by [ɾən] and then [dən]. But there is a fair amount of variation among speakers—and even within a single speaker: you can hear her use [dn̩] here right before the sentence in question—so you probably need not worry so much about it so long as you can produce at least one of the three options.