Jonathan isn't fully convinced his father Saul is set on killing David, but David is.
Jonathan covenants with David's house, against his father Saul.
At the next feast, David is intentionally absent, to see if Saul will be mad. He is and takes it out on Jonathan, trying to kill him with a spear like he did David. Jonathan goes out and keeps covenant with David, telling him of Saul's intent and sending David away.
David flees to Nob, where priests live. He gets bread from before the ark for his journey, though it is meant only for the priests - an exception can be made for this. He also takes Goliath's sword. He flees to Gath (where Goliath was from, with his sword!), but they recognize him as their enemy. So he acts crazy and useless, and thus gets away.
How this is about Jesus
Israel's leaders sought to arrest Jesus many times, but He escaped.
Prominent Israelites sided with Jesus against the installed rulers, like Jonathan did: Joseph of Arimathea, Nicodemus of John 3. They also received anger and threats, as Jonathan did (John 7:50-52).
Jesus refers to David eating temple bread when the Pharisees accuse Him of breaking the Sabbath. He assumes He is on David's mission, fleeing the bad guys, and He is! (Matthew 12:1-8)
He remains silent before Gentiles who could kill Him. Being greater than David, instead of avoiding death in exile, He accepts it and so saves the world (Luke 23:8-11).
Work together with God's people and leaders. Protect and help each other.
Sometimes good deeds done in the past, help you in the future in yet unknown ways (Goliath's sword).
Enemies can arise from unexpected places (Saul).
When desperate for help, don't be foolish about who you take refuge with (Achish).