I have ordered numerous times from iherb for CoQ-10, Turmeric and other things. Normally the site tells me when I get over the limit for the free shipping as the totally cost to high by this amount or to much weight. So I adjust the order. Only one problem when I ordered two separate shipment on the same day. The first order arrived in about 9-10 days. The second was missing.
Contacted iHerb and they refunded the amount but informed me from then on free shipping to Thailand would not be refunded until the order arrived back to the store because they can't track the shipment. Just checked my orders and I see it did return finally. The last order of 6 items I paid $8.37 shipping. All orders delivered to by door here in Nonthaburi with no problem.
As for Zinc, I have purchased from the small drug stores with no problem along with anything they have on the shelve (not behind the counter). I would suggest going to another store.
I have also brought back large amounts of vitamins, prescription medication from Tricare and the VA in checked bags with no problem. The only time bag was ever checked was by TSA some where before Thailand. Found the note/letter in the bag when I opened and nothing missing. Just we checked your bag.
I have a friend who gets a year supply of his prescription meds at a time in the US and brings back with no problem. Now that we no longer have an APO, so no way for Tricare to ship to Thailand so may try the same.