Where do military aircraft carry flares?
The location of the flare/chaff dispenser (FCD) depends on the aircraft type and even in case of the same aircraft, they can be located in different place, depending on the version and customer.

For example, the F-16 carries the FCD in its body fairing, as can be seen in the following image of Hellenic Air Force F-16 Demo Team “Zeus”.


Image from theaviationist.com

The following image shows a close view of FCD.


Image from f-16.net, credited to Capt. Lance

The following image shows an Israeli F-16B 'Nezt' having FCD between its ventral fins.


Image from theaviationist.com



Initially, most of the FCDs were retrofitted to the existing aircraft and were simply attached to them. However, most of the modern aircraft have FCD bays integrated into their fuselage. Still, some aircraft can carry extra flares/chaffs in their pylons (called PIDS (Pylon Integrated Dispenser System)), as shown below in an RDAF aircraft.


Image from f-16.net, credited to Erik Frikke



Also, most of the combat aircraft have the FCD in the bottom, while transport aircraft (and helicopters) have them on their sides.