If I move into a battlefield with Traveling Merchant and discard Flame Chompers, can I play it as an attacker?

No, you cannot play Flame Chompers as an attacker in this situation.

According to RiftJudge FAQ #5319, when you move Traveling Merchant to an unoccupied battlefield, you do not control that battlefield until the movement fully resolves. Because Flame Chompers' ability triggers and resolves while the Traveling Merchant move trigger is still on the chain, you do not yet control the battlefield to which you are attempting to play the Flame Chompers.

Sequence:

1. Move Phase: You perform a Standard Move with Traveling Merchant to the open battlefield.
2. Trigger: Traveling Merchant's "When I move" ability triggers and is placed on the chain.
3. Chain State: The game enters a CLOSED state (the chain exists).
4. Resolution: You resolve the Traveling Merchant trigger by discarding Flame Chompers.
5. New Trigger: Discarding Flame Chompers triggers its "When you discard me" ability, which is placed on the chain as a new pending item.
6. Legality: When you resolve the Flame Chompers trigger to play it, you must select a valid location. Since you do not yet control the battlefield (you are still in the process of moving and resolving the chain), you cannot play the Flame Chompers to that battlefield. You would need to play it to your base or another battlefield you already control.
7. Combat: Combat (and attacker designations) only begins after the chain is empty and the move fully resolves. By that point, the Flame Chompers must have already been played, and it cannot have been played to the battlefield you were moving into.

As established in RiftJudge FAQ #10656, you cannot play units to a battlefield you do not control; playing Flame Chompers to a location you do not control is illegal.