Does salt activate or inhabit amylase activity?

Yes, I believe salt plays with its shape.

Can you give us the reference to the article you referred to?

When you say 'salt' I assume  you mean sodium chloride, NaCl. The word 'salt' in chemistry refers to any compound formed from a metal cation and a nonmetal anion like chloride, sulfate, carbonate, etc.

The activity of an enzyme depends on temperature, pH, cofactors and its substrate as well as ions such as calcium or phosphate. You can inhibit ANY enzyme if you add enough NaCl to the reaction. It is not scientific to say 'salt inhibits amylase'. You need to specify what kind of salt and how much.

Human blood and tissue fluid contains NaCl normally and this does not inhibit the body's enzymes. But if you tried to do an enzyme reaction in a test tube and added a high concentration of NaCl, the enzyme would probably not work. Eating too much sodium can be bad for your circulatory system but most of the excess is excreted by the kidneys.

Human salivary alpha amylase happens to be one enzyme that has a chloride binding site and is activated by chloride: http://www.jbc.org/content/271/39/23836.full.html
Once it is activated, however, adding more NaCl will not activate it further. So, if you put a lot of salt,  sodium chloride, on your potatoes, the amylase in your saliva should still be able to convert the starch into sugar. You could test this by comparing the sweetness you experience from keeping a piece of unsalted cracker in your mouth compared to one that has salt on it.

Let me know if you have more questions.

I meant table salt (NaCl) when I mentioned salt. I'm assuming it's what you used.

I believe what salt does, and I'm basing this off speculation alone, is that the ions interact with the amino acids that make up the enzyme. This changes the enzyme's conformation, preventing its active site from interacting with the substrate.

You'd have to do a PubMed search to find the reference: https://biology-forums.com/index.php?action=pubmed