A player cannot discard a card for its free action and then immediately tuck it for income during the same turn. According to the rulebook:

• "When a card is used, it is used for only one of its benefits. For example, if you play its effect as your main action, you cannot discard it for its free action." (page 7)
• Discarding a card for its free action means the card is no longer available to be tucked for income, as it is removed from your hand and placed in the discard pile.

Therefore, once a card is discarded for its free action, it is removed from play and cannot be tucked for income.

Source: page 7

Source: Core Rulebook (pp. 14, 15, 19, 28, 7)