"Destruction Jammer" cannot be chained to the activation of the Ignition-like effect of a Continuous Spell or Trap Card (like "Skull Lair", etc.).
"Destruction Jammer" cannot be chained when "Premature Burial" or "Call of the Haunted" is activated because they do not destroy a monster card at that time, nor can it be chained when the Special Summoned monster is destroyed.
"Destruction Jammer" cannot be chained to effects that may or may not destroy a monster, like "Acid Trap Hole", "Blowback Dragon", "Magical Dimension", "Reign-Beaux, Overlord of Dark World", "Snipe Hunter", etc.
"Destruction Jammer" can be chained when the effect of "Light and Darkness Dragon" to Special Summon a monster is activated, but not if the owner of "Light and Darkness Dragon" has no monsters on their side of the field.