Your combats are likely too hard
A single flind is CR9, which alone is a deadly challenge for 4 5th level characters (5000xp whereas the deadly threshold is 4400xp), and in melee has a +9 to hit which is quite high.
If this was the 'boss' encounter of the day, after a series of easier encounters then that is fair play, but if the player is going down in every combat then quite simply your combats are too hard.
A CR5 creature is meant to be a medium challenge for a group of 4 level 5 PCs. I would suggest not really picking a creature with a CR above the party level, especially if you are also adding extra mooks which make combats much harder due to the action economy.
If you look at the starter adventure lost mines of phandelver, the hardest fight (for groups up to level 5) is a young green dragon, which would be solo, is CR8 and often the advice is to talk to it and avoid the actual combat encounter. It is also specified to fly away at 50% HP which is a pretty big deal when it comes to encounter difficulty.
How to fix it if you don't want to change the combats
I can understand wanting to use powerful enemies, but you need to help your party out by increasing their power accordingly. At level 5 it is perfectly acceptable for this paladin to be in plate armour, with a shield, and having an AC of 22 including shield of faith. My own paladin in this situation multi-classed into warlock to get access to the shield spell as well, taking AC up to 27 whenever I needed it.
Because I liked to tank I rarely used spell slots on smite, and instead preferred to use shield to stay alive.
You might also want to review the party and ensure they are using effective tactics. A flind for example has 30ft movement, and unless you started the combat that close and the flind won initiatve, someone in the party should have done something debilitating to the flind to prevent it getting straight into melee, get a few rounds of ranged attacks off and weaken it before it closes in.
You might have a party where everyone thinks damage is the be all and end all, which is isn't, especially against such a powerful enemy.
Your wizard could cast slow, your warlock could keep it at bay with repelling blast etc. There are all sorts of method.
Your paladin player might like to get straight into melee, but that isn't an efficient tactic, and if you are sticking with difficult combats then they need to be more sensible.
Lastly I would suggest letting the paladin respec, maybe they could do with a CON boost, or let them take the average HP instead of rolling, or like I do give max HP for the first 3 levels to ensure the 'tanks' have that HP buffer they often rely on.
To address how to be tankier
I have looked at playing melee tanks before, and concluded that most classes just are not good at it. AC20, or 22 with standard gear doesn't cut it against difficult foes in my eyes, and as levels go up the + to hit from enemies begins to scale faster than +AC.
As such you have to turn to magic.
My paladin tank, which is the only character I have ever created that I would consider actually tanky, is an oath of conquest, with a level of hexblade.
Hexblade means I can skip STR and become SAD (single attribute dependant) instead of MAD (multiple attribute dependant), which allows for higher CON.
It also gives me a short rest spell slot, and access to the key spell; shield.
Conquest paladin means I use fear liberally which gives enemies disadvantage to hit me.
So I have an AC up to 28 when I need it, a +5 bonus to my aura of courage for amazing saves and can afford to keep my STR at 15 which allows for more HP.
I would suggest you let your player make a similar build, because otherwise sticking to 'standard' builds against the combats you seem to talk about just won't work.
I would even caution against this, because I recently did a level 20 fight and the crazy attack bonus' at that level meant that I still got hit more often than not, and actually just sticking within 30ft and giving my aura of courage (plus my aura from my holy avenger) was more use to the group than anything else I could do. D&D simply doesn't allow for proper tanking against anything that wants to kill you.