There are only two ways to improve the damage done by spells:

ONE:
Garnet and Eiko's summon spells are stronger if they have learned and equiped the ability "Boost." Boost makes makes the "long version" of the summon animation appear every time, and thus the summons have stronger attacks. Boost can be learned from a Pumice Piece, I believe.

TWO:
If Vivi uses the "Focus" command before casting a spell, his spells will be stronger.

Once a spell is learned, it is not dependant on the item it was learned from. Keeping a peice of equipment on doesn't increase the spell's attack. Any other strengthening of the spell would come from the general buildup of stats, i.e. learning Magic+20% or similar abilities.