The Sword of Sharpness has a utility as a magic item that is somewhat variable in that it depends on the player who has it, and on the DM. We'll take the features one at a time.
This is fluff. Moving on.
Maximized damage against objects
The utility of this depends on the player and how creative they are in using it. If you never attack an object, this is pretty much useless. However, you can get a LOT of mileage out of attacking objects. Personally speaking, I've busted my way through walls to circumvent an ambush or trap. Cut the hinges off a door so I could remove it without destroying it (the rogue broke the lock while trying to pick it). I've cut ropes to drop chandeliers on my enemies, busted holes in an enemy's boat so we could escape while they sank, and wrecked the DM's death traps by destroying the mechanisms that made it work (he wanted us to go through this complicated disarming process...I worked all the delicate looking moving parts over with a Maul. It worked). Those scenes that turn up where, say...Wolverine carves his way through a wall with his claws? With a Sword of Sharpness, you can do that.
The ability to reliably deal maximum damage to objects, and reliably overcome most objects' damage thresholds if they have one, is really useful in the hands of a creative enough player.
Ask your DM about the environment, look around, think about what you can do with what you can destroy. That door doesn't have to be the only entrance...those light fixtures can be weapons.
Again, this is all stuff you can do with an ordinary weapon...but a Sword of Sharpness is much more likely to finish the job in fewer attempts.
Boosted damage on a Nat 20 is nice. Barbarians, for example, are partially built around their boosted crit damaged. And, per the DMG, it's a flat +14 damage on a nat 20, which has more reliability than 4d6, even if it has lesser peak damage output. To address your comparison to the Flametongue...bear in mind that the Flametongue's bonus damage is Fire Damage: one of the most resisted damage types in the game.
Here is where we hit DM caveat territory. What does it mean to dismember a target? Well, per the DMG, that is going to depend on your DM, and it's going to depend on what you're attacking. If you take a limb off a Zombie or a Troll...no big deal. If you take a limb off something that is living and doesn't regenerate at an insane pace...they are in trouble. Let's walk through what happens here, realistically.
- You lose the use of that limb. Depending on if this was a leg or arm, it has a different impact, but it's simple enough to figure out.
- Here's the important bit. You immediately begin hemorrhaging blood rapidly. Taking an arm off severs the brachial artery, taking a leg off severs the femoral artery. With the degree of blood loss this would cause, you will be dizzy and drowsy almost instantly, unconscious within seconds, dead within a minute or two. They'll last longer if it is a 'clean' amputation (perpendicular to the line of the limb) because arteries can pinch themselves shut...but that doesn't work if the cut isn't straight across, and since this happened in combat, you probably didn't give them a nice perpendicular amputation. And even if you did...that level of damage and pain is going to put just about anything into shock...which, however the DM portrays that, certainly puts them out of the fight entirely.
Now, is your DM using it this way? That's DM caveat. But in a game that I am running, limb loss = immediate removal from combat and massive ongoing damage. Unless medical care is administered immediately, the victim of that attack is going to die. Ultimately, in one of my games, the difference between a Sword of Sharpness taking a limb, and a Vorpal Sword taking your head is whether or not you have a chance to save the victim before they bleed out.
If you don't come up with creative uses for your newfound ability to obliterate inanimate objects and your DM treats limb loss like an inconvenience, then I would agree with you that the Sword of Sharpness probably doesn't deserve its Very Rare rating. But if you get creative, and your DM treats limb loss like the catastrophic injury that it actually is...then it rates quite a lot better. And...+14 damage on a nat 20 is pretty significant (equivalent to average damage of a 13th level Barbarian's Crit damage bonus with a Greataxe), and since it is Magical Slashing damage, very few things are going to resist that.
I would personally rate this on the lower end of the Very Rare magic items...but I still think it deserves the title
Since nothing about weight is mentioned and the boots give you flying speed equal to your walking speed, I would assume that the regular carrying capacity rules are in effect (page 176 of PHB). You can carry 15 times your strength (including your equipment etc), or push, drag or lift 30 times your own weight. If doing the latter and the thing you move is heavier than your carrying capacity, you will have your speed reduced to 5 feet.
It might feel a bit silly that winged boots are affected by your strength, but I think it's RAW.
The intent is probably that only whoever activated it can use it.
Activation requires physical contact. From my reading, this intent is given by the use of you, in every sentence. Usually it would be unclear who exactly is "you", but the earlier sentence defines it (as the person who stood astride and spoke the command word).
The wording, if it was intended that any creature could use it, would probably be "A creature that says the command word", for example.
As an additional conjecture, it would be silly that anyone hearing the command word could mess up the item easily like that.