Goblin Kaboomist is in the same deck as Gift of Immortality, and to a larger intended state of affairs, Feldon of the Third Path. Do these cards synergize in any boonful fashion?

Yes, Goblin Kaboomist has synergy with both of those cards (but not at the same time).

If you have a Goblin Kaboomist enchanted with Gift of Immortality, the Goblin will come back every time you lose the coin flip. (If it somehow dies again before the beginning of the next end step, it will be gone for good, since Gift of Immortality hasn't come back yet.)

If you have a Goblin Kaboomist in your graveyard, you can activate Feldon of the Third Path during your opponent's end step (or in multiplayer, the end step of player who goes just before you). Then the Kaboomist token will trigger on your upkeep.
Note: You have to do this before your turn begins. If you activate Feldon during your upkeep, you won't get the token's upkeep trigger.

Thanks for the clarifications, CommanderJim. That sounds better than I thought it would pan out. Glad to hear the Kaboomist with the Gift on it doesn't recursively make more and more land mines.