Why does my LED light flicker when turning it on using a dimmer switch?
Connect it electrically the same as before
Based on the pictures, the original connection was:

TWO black wires to one screw
A blue wire to another screw

In that case, the blacks are both hot. One is the incoming hot, the other is an outgoing hot to another location. That is a little odd because there is already a wire nut, so instead all those wires should have been connected using the wire nut with just one short wire (pigtail) to the screw. Under most circumstances, you should only have one wire per screw.
The blue wire is switched hot.
The new dimmer only needs two wires, unless it is used as part of a 3-way switch (i.e., 2nd switch elsewhere).
The instructions are not terribly clear in certain respects. However, it is pretty clear that for a single (not 3-way) switch, it does not matter which wire goes in which screw, as long as you put one wire on one color screw and another wire on a different color screw. Therefore, you put a black wire (just one, more below on that) on the screw that is a different color from the other two screws and the blue wire onto the screw opposite that screw (i.e., other side of switch rather than above it on the same side of the switch). That gets you hot and switched hot connected properly.
Now to the second black wire. The instructions actually say &quot;Your wall switch may have two
wires attached to the same screw. Tape these two wires together before disconnecting.&quot; but then never (as far as I can tell) actually says what to do with the taped wires. Taping is not a valid way to permanently connect wires, and I don't think they actually meant &quot;tape together electrically&quot;, but rather &quot;tape together so you know where each of these wires that all look the same should go&quot;. In this particular situation, what you need to do is wire nut the two wires together and attach a pigtail (short piece of same colored wire) to the screw. Since your picture already shows a wire nut &amp; pigtail, all you actually need to do is move the &quot;extra&quot; wire (the one that was originally on the screw and is not a pigtail) to the wire nut with everything else.
By connecting one black to one brass screw and the other black to the other brass screw, you effectively treated your hots (plural) as if they were travelers (used between 3-way switches). What that actually did (I think) is something like:

switched hot became &quot;common&quot;
hot (incoming) became &quot;traveler 1&quot;
hot (outgoing) became &quot;traveler 2&quot;

When switch is in &quot;traveler 1 ON&quot; mode:

common connects to traveler 1 == Light on
traveler 2 OFF == something elsewhere in the house isn't going to work

When switch is in &quot;traveler 2 ON&quot; mode (which is the same as &quot;traveler 1 OFF&quot; == &quot;just flip the switch&quot;:

traveler 1 OFF == Light off
common connects to traveler 2 == everything else in the house works normally

As far as the blinking when turning on the light, I suspect that is simply the way the bulb is handling the initial signal form the dimmer. It is possible that other bulbs will work better, but hard to say. Dimming LEDs is a tricky business - almost amazing that any of them can dim at all when run on AC.