The effect of "Dragunity Phalanx" which Special Summons it while it is treated as an Equip Spell Card starts a Chain. This effect is treated as the effect of a Spell Card, not the effect of a monster.
The effect of "Dragunity Phalanx" which Special Summons it while it is treated as an Equip Card is activated as the effect of an Equip Spell Card. Thus, if "Imperial Order" is active, then the effect is negated and "Dragunity Phalanx" is not Special Summoned.
Suppose that "Dragunity Phalanx" Special Summons itself from being treated as an Equip Card, and then during the same turn it is removed from the field (for example, send to the Graveyard) and becomes an Equip Card again. In this case, you can activate the effect of "Dragunity Phalanx" a second time, and Special Summon it again.