Are you referring to instruments as used in classical orchestras playing "Western" music, or to traditional folk instruments used by different cultures?

Because, to stay with your example, there is actually quite a variety of flute instruments even today if you include those not usually found in a symphony orchestra. The common elements between those instruments are mostly caused by physics - say, in order to be able to produce several different notes from a flute, you'll need to make holes into it that you can close and open with your fingers. You also need to get the air inside moving in a certain way, and there are a limited number of ways to do this.

There are a lot of misconceptions in this question that I'll deal with a few of:

• Most instruments don't look exactly the same, and don't play the same way, even today
• They would have looked less the same and been greater variations in the pre-industrial age

So rather than addressing every instrument ever made (because that would take thousands of pages of text and more research than I care to do ever), I'll address the example you gave - the flute.

First, I'll get you to read the history I wrote about the evolution of the flute: https://www.reddit.com/r/AskHistorians/comments/3ec872/i_have_read_j_j_quantz_revolutionized_the_flute/

So, you're asking about hundreds of instrument makers all coming out with different designs, when it was pretty much one dude. Boehm invented the modern flute pretty much single-handedly, and everyone just copied his design. The designs he made in the 1800s are virtually identical to the way they are now. Other than using newer, more durable materials, the Theobald Boehm flutes could be played by just about any modern player.

So it wasn't some international consensus of standardization - it was just him. He came up with something awesome by himself, and everyone else just ran with it.