League of Legends (LoL) Question: bootsof swiftness viable?

Nope they aren't, for the simple reason that tenacity does the job better:

Consider being 50% slowed for 1 second. Then, you'd cross 50% of the distance you'd normally do.
Tenacity would make this 50% slow for 0.65 seconds. Means, you'd cross 67.5% of the distance you'd normally cross.
Swiftness passive makes this a 37.5% slow for 1 second. Means you'd cross 62.5% of the distance you'd normally cross.

Conclusion. Even against a full slow-based team, Tenacity will always outclass Swiftness. If you aquire Tenacity through alternate items rather than Mercury's Treads, you could consider them against high-slow based teams. However, there aren't many teams like that out there and the other tenacity items are kinda bad atm.

Yes. Try them on jungle and top cho'gath.

I really think they are outclassed by every other type of boot, but they have a teensy tiny place, although with the new 'alacrity' enchantment, boots 3 are even more fringe. I know for a fact that bruiseleet runs them on 90% of his cho'gath games.

Outside of cho, though, I can't think of any champions that would benefit from boots 3 over other boots.

Boots of Swiftness is a strong item on jungle Udyr. With a Spirit of the Ancient Golem, BoS gives Udyr the most cc reduction possible. This helps with Udyr's perennial issue of being kited

I would find this more useful if you were dealing with champions that slowed you down a lot, such as Nasus and Ashe. In either case though, tenacity is a better perk to have overall, and Boots of Swiftness aren't really viable.

Boots of Swiftness are viable on Vi. cause Boots of Swiftness reduce the slow by 25% but he also reduce the slow from yourself so you can run when you charge your Q.
P.S. sorry for my very very bad english