What is the maximum time for which the dough should be allowed to rest before making Parathas?
Why resting longer?

Resting the dough not only let's gluten linking begin, but also allows enzymes to "transform" starches into sugars. There are some technics for making bread that take profit of that to extract more taste from the wheat, such as autolyse (invented by Raymond Calvel) or Pain à l’ancienne (which uses autolyse and other delaying methods that you won't use in not leavened breads).

Originally Monsieur Calvel stated an autolyse time of between 20 and 40 minutes (that link might be in Spanish, but I don't understand why it's not in English), but nowadays people are experimenting with 2 hours, and even 4 or 6 hours of autolisis.

That enzymatic activity won't be affected by lipids, so adding fat or oil for Parathas or Rotis will work the same. They can be affected by a PH&lt;4 or 3.3, but I don't think you'll reach that PH in a Paratha's dough.

So, how long is too long?

The longer you let enzymes make sugars, the tastier the dough will be. But if you rest too long a dough, the gluten will finally get broken: the dough will look more like a puree than a kneaded dough. It will depend on the enzymatic activity of the flour, and can vary a lot from one flour to another. It is measured by a value called falling number (you can see why is it important here). 

That index is very rarely labelled in packages, but you can try getting in contact with the millers and ask them. Or you can also try to find the answer to your question empirically for the brands of flour you use (that value shouldn't vary from different batches of the same brand of flour). Touch the dough every hour to feel if it still has a workable consistency.

Note that your dough will be stickier, due to the sugars released by autolisis.