Well you have 2 ways to shoot down F-15's in the game:
1- in the aircrafts folder go to F-15 DATA.ini
[ECM]
SystemType=ECM_JAMMER
JammerType=DECEPTIVE_JAMMER
JammerStrength=60.0 <<<<<<<<<<<<<<<<<<<<<<<<<<<<<< lower this number
MinFreq=2.0
MaxFreq=20.0
CanJamCW=TRUE
[DecoyDispenser1]
SystemType=DECOY_DISPENSER
EjectPosition=-1.13,1.40,-0.88
EjectVelocity=-2.59,0.00,-9.66
NumChaff=60 <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<< and this one
NumFlare=30 <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<< also this
[DecoyDispenser2]
SystemType=DECOY_DISPENSER
EjectPosition= 1.13,1.40,-0.88
EjectVelocity= 2.59,0.00,-9.66
NumChaff=60 <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<< and this
NumFlare=30 <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<< finally this one too
but to me its cheating
2- AMBUSH them, fly as low and fast as possible when u get close enough zoom climb, lock, and fire, get as close as possible to ensure a hit. this surprise attack technique always works with me, because if they see u they cannot fire at u or when they fire their missiles will hit the ground, ground clutter is better than ECM sometimes.