Ok, first: "Blitzkrieg" was invented by the allied nation's media as a term for the rapid average rate of advance of german forces, especially armored divisions. (To the german commanders, what they did wasn't so much a special kind of warfare. It was just the logical continuation of the way war had been changing since the Crimean War.) German forces achieved those rapid successes due to implementing many assorted tactics and principles that had been concluded from the lessons of WW1. The allied nations did not implement these new ideas fully, even though Britain actually came up with many of them first.

As to why Germany implemented these ideas and the allied nations didn't: the canonical answer is that since it was dismantled after losing WW1, the german army did not have as much of an entrenched an "old guard" of conservative staff officers. Thus relatively young and innovative officers could build up the new german army under entirely new principles. However I would add to that the fact that the prussian army and the german imperial army that succeeded it had been strongly encouraging innovation, which allied armies simply did not do to that extent. Many key elements of german success in the early offensives had been developed as early as the first decade of the 20th century, i.e. even before WW1.

I read somewhere that the key tank tactics used by the germans in battle were actually brought up by Charles de Gaulle. In 1934 he wrote Vers l'Armée de Métier (Toward a Professional Army), were he advocated pure mechanized divisions, instead of (what most armies did) putting a few tanks for support in infantry divisions. It were the purely mechanized divisions, fast moving and powerful, who could make 'sickle' movement and trap the immobile infantry divisions, cutting off their supply lines.

I don't know who specifically brought up the other important thing, the divebomber.