Yes, players are allowed to use the resource exchange free action multiple times per turn, and exchanges can be chained.

This is supported by the following points from the rulebook:

• On page 18, under "Resource Exchange," it states:
  "During your turn, as a free action, you can exchange 2 cards, 2 credits, or 2 energy for 1 card, 1 credit, or 1 energy."
• There is no restriction mentioned on the number of times this free action can be performed per turn.
• The rulebook also clarifies (on page 7, under "FREE ACTIONS*):
  "Free actions can be performed at any time during your turn – before, after, or even during your main action."

Therefore:

• You may perform the resource exchange free action as many times as you wish during your turn, as long as you have the resources to do so.
• You may chain exchanges, such as exchanging two cards for a credit, then using two credits for an energy, within the same turn.

Source: page 18 (Resource Exchange), page 7 (Free Actions)

Source: Core Rulebook (pp. 18, 19, 28, 7, 9)