LNK304 AC/DC converter - pulsing output
Your output inductor L1's magnetic core is saturating.  You might not be able to see it, but trust me, there is a tiny ferrite rod with a winding around it inside the resistor-style axial body.  1mH at 280mA requires an inductor that is simply not possible to fit into something as small as your little resistor style inductor. 

When the supply turns on, the output capacitor is a low impedance load until it is charged, and the bias current (with super imposed ripple current) ramps up until L1 saturates, causing a massive and sharp loss of inductance.  The high inductance is what limits the current through the output MOSFET.  This would likely appear as a short, which triggers the LK304's fault protection.  They claim this will turn off the MOSFET for 800ms, though oscillator variation is enough to shorten that. The 3.3kΩ resistor needs only 330ms to discharge whatever was built up in the output capacitor, and this is the source of your pulsating output.

Please use an appropriate component for L1.  It's probably the most important component in the entire circuit, it is not acceptable to just toss in whatever you find.  If it doesn't have a datasheet with an exact saturation current specified, then it shouldn't be in this circuit.