Some body armor is restricted by ITAR, you need an export/import license for it. Rifle-rated plates and some ceramic inserts are ITAR.
There is a temporary exemption in some cases: http://www.canzonerilegal.com/itar-travel-advisory-body-armor/
Stupid part of it is that there is nothing stopping him from buying it once he got here. Body armor is not regulated in most places in the US.