The conflict in the story is Jonah, Charles Lindbergh, and the Time Travel Agency verses Gary and Hodge. The problem between the two sides is that Gary and Hodge disregard the Time Agency Rules and travel to the past to steal a historical icon, that being Lindbergh's son. Jonah is involved because he is believed to be the stolen child from history.
Gary and Hodge go back in time to steal Charles Lindbergh's famous baby in 1932. This builds up to the climax in the story because Gary and Hodge are breaking the agencies rules by changing past time causing more tension between the two sides.
Lindbergh looks for his "dead" son in 1932, and with no luck, writes a note for a time traveler to see from the future, hoping they will save his son. Gary and Hodge see this note and lure Lindbergh in to help them fight against the time agency. This leads to the climax of the story because the two sides of the conflict will meet.
Gary and Hodge seek help from Lindbergh, saying if he helped them steal more famous children from history, they will give him his son. At this point, Lindbergh is no longer on the Time Agencies side, and is now an antagonist which turns the story in a new direction.
Jonah time travels onto the plane Lindbergh is flying through time to go and steal more famous children from history. Jonah convinces Lindbergh to turn against Gary and Hodge once again by revealing that he himself (Jonah) is his son and never died, and that he was just in a present time period, brought there by kidnappers Gary and Hodge. At this point, the protagonists have the upper hand against their enemy, and gain control of the conflict.
Lindbergh decides to fly back to original time to disregard Gary and Hodges orders. With Lindbergh no longer on their side, Gary and Hodge's plan fails, and they are caught by the Time Agency, and put in prison. Jonah goes to live his normal life in the twenty first century, and Lindbergh goes back to 1932 knowing the true story about his disappearing son. The conflict is now resolved because Gary and Hodge are locked up and the protagonists win.