Flecktarn was developed by the (West) German Bundeswehr in the 1970ies, but full scale introduction to the armed forces did not take place until 1989. It's official name is "Fünf Farben Tarndruck" (Five colour camouflage).
What we now know as Flecktarn was chosen among a number of different patterns that were evaluated against each other.
Some claim that the Flecktarn pattern is developed from Waffen-SS patterns used during WW2 - like the pea pattern (reproduction) shown below:
I don't think the patterns are that similar, but the German engineers might have been inspired by the older patterns.
Denmark - first foreign user
The first foreign user of the pattern was Denmark. In 1978 the Danish Army tested the T/78. The pattern was in 1984 introduced full scale in the Danish armed forces as M/84. The colours of the M/84 is reduced to only three: dark green, light green and black as opposed to the five colours of the German pattern.
Other foreign users
China uses a version of the Flecktarn for its "Tibet" pattern - as the name implies this is worn by Chinese troops in Tibet:
The pattern has also been used (still in use?) by Polish Police SPAP anti-terror units (SPAP = Samodzielny Pododdzial Antyterrorystyczny Policji), the pattern is called "wz. AT-1 Plamiak" (Plamiak means "spotty").