And can it still perform both of it's slam attacks while holding one?
For Reference: http://archivesofnethys.com/ClassDisplay.aspx?ItemName=Phantom
The phantom cannot wear armor of any kind, as armor interferes with the Phantom's connection with it's master. It also cannot use weapons, for.. some nebulous reason. There is no mention about shields.
On top of that, unlike an Eidolon's slam which specifies that the Eidolon can only have as many slams as it has limbs (arms), there is no such restriction on the Phantom. Can the Phantom slam while it's arms are occupied? Like some kind of kick or body check? Even Oozes can slam, after all.
Except for amorphous creatures like oozes, slams seem to be limited to one per limb. I don't think you could use an ordinary shield with a limb being used to slam, though a buckler could work.
As to whether a phantom could use a shield at all - since they can't use armor or weapons I'd say no. Armor is often shorthand for 'armor and shields' in PF, and it's hard to see why they'd be able to use shields but not weapons too.