The ampere is a measure of flow of charge per unit time. Talking in terms of "amps every x minutes" does not make sense.
From reading online sources, understand 3600mAh is 3600mA per hour but still don't understand @0.2C.
No, it's 3600 mA for one hour. 3600 mA × 1 h = 3600 mAh.
Or 1800 mA × 2 h = 3600 mAh.
Or 7200 mA × 0.5 h = 3600 mAh1.
My question is, If I decide to use 5 * 18650 cells in series, 3600mAh @0.2C discharge for one BQ77915 device, is this 3.6A * 5 = 18A every 12 mins?
Again, "18 A every 12 mins" doesn't make sense. Instead, since all five cells are in series they will all pass the same current and have the same Ah capacity. 3600 mAh @ 0.2 C = 3600 × 0.2 = 720 mA discharge rate. At 18 A the discharge rate would be \$ \frac {18}{3.6} = 5\ \text C \$ (which would be 25 times the 0.2 C discharge rate).
The fact that there are five cells in series will raise the voltage to five times the cell voltage but does not increase the current capability.
Looking through the design details the example says "The battery allows 4A continuous current."
Then that's the most current you can draw from one, two ... or five series connected cells. If the cells are 3600 mAh then we can work out the discharge time as \$ t = \frac {capacity}{current} = \frac {3.6}4 = 0.9 \ \text h = 54 \ \text{min} \$ (subject to note 1 below). You might want to work on a time of 30 minutes for such a high discharge rate but the datasheet should help you work that out. Don't forget to allow for aging of the cells too.
Note that the above result is read as "4 A for 54 minutes".
1 I'm simplifying here. At higher discharge rates the battery becomes less efficient so effective capacity is reduced. Hence the 'C' rates.