The weapons will deal their normal, magically-enhanced damage. Minus 5, for the golem's DR, unless the weapons are also adamantine. Immunity to magic doesn't automatically destroy all magic the golem comes into contact with, it just can't be directly affected by magical effects.
Immunity to Magic (Ex)
A flesh golem is immune to any spell or spell-like ability that allows spell resistance. In addition, certain spells and effects function differently against the creature...
If something allows spell resistance, immunity to magic functions like infinite spell resistance against it. Things that aren't stopped by spell resistance (like sword swings, acid arrows, and being crushed under a ton of solid rock during an earthquake spell) aren't stopped by immunity to magic. It also specifically only works against spells and spell-like abilities, so it doesn't stop things like dragon breath or magic swords.
So we've established that "immune to magic" doesn't turn off a magic weapon's +1. What does that mean for the golem's DR? In this case, nothing.
Weapons with an enhancement bonus of +3 or greater can ignore some types of damage reduction, regardless of their actual material or alignment. The following table shows what type of enhancement bonus is needed to overcome some common types of damage reduction.
Cold iron / silver +3
So the weapons would need to be +4 to bypass the golem's DR 5/adamantine. If they were +4, they would overcome the DR despite the golem's immune to magic trait; but it's a moot point since they're only +1 weapons to start with, therefore they only overcome DR /magic (and the various damage types for their weapon types).