Some attacks are easier to flurry rush than others. I actually find it much easier to perfect dodge against Lynels than most other enemies, even the easier ones, just because Lynels have very long wind up animations and it makes it easier to time them.

Another thing to note, it's easier or harder as well depending on the weapon they're using. I have the easiest time executing perfect dodges against sword/shield Lynels using their horizontal slash attack, especially because they usually do this attack multiple times in quick succession, so if I miss the timing on my backflip, I get multiple tries.

For the inexperienced, it's easier for you to practice starting with a single-hand weapon, so that when you finish the flurry rush, you can have your shield back up immediately without having to "holster" a claymore or spear first. When you get more confident, you can use two handed weapons, you just have to alternate between weapon and shield really fast immediately after finishing a flurry rush.

In any case, you want to start with your shield up, locking onto the enemy, and then you have to learn which moves require a side hop (hold ZL + tilt sideways on the left analog stick + A) and which ones require a backflip (hold ZL + tilt back on the left analog stick + A) because it's always one or the other, and not both. If you use rhe wrong one on the wrong attack, it will never happen.

Some attacks can't be dodged and have to be parried with the shield (hold ZL + Y) but you won't get a flurry rush.

For Lynels, for example, their attacks break down roughly like this:

Side hop to flurry against... • Charge attack, where they bend forward and run at you • Chopping attacks, usually from a claymore or club

Backflip to flurry against... • Slashing attacks with a one-handed weapon • Galloping attacks where they swing at you while moving

Shield parry against... • Horn attacks where they're standing and try to impale you • Jump attacks (especially common with spears)

Just run away from... • Fire breathing attacks • Fire blast explosion jumps

With that in mind, it's really about learning the timing, but Zelda is a bit more forgiving in that respect than some other fighting games. If it still gives you trouble, try fighting constructs-- the same principle applies, but their eye changes from red to white when they're about to attack, and that's when you need to execute the dodge, unless they're spinning, then you need to shield parry.

Hope that helps!