If I have a specified number of light sources with known luminous flux and opening angle pointing in the same direction and with known distance from eachother, how can I calculate the total luminous flux?

 

In a specific problem I have a 100 LEDs with 22 candela and a 20° opening angle which I calculated to give me 3300 lumen per lamp. However now I am unsure how much light the combined hundred lamps (aranged in a grid with 1cm distance) will give - as I strongly assume it wont be just 330.000 .

You'd need to know the area over which the light will spread. For a point source it's easy, since it's a 1/r² dependence, but for your 20° angle, you'd need to know something about the intensity dostribution within that angle. However, if you are far away from the grid, so that it's approximately a point source ("far" meaning several times the 9 cm size of the grid) it should look a lot like a single LED with the total power of all of them, spread over the 20° angle.

The light will spread over approximately 40cm² per LED, in all they should cover about 280cm², where of course some overlay will occour...here is an interference image I created (the dots have 1cm distance)