Kom, so you know, Vel'Koz has some pretty heavy mana issues early game since you need to spam his W for harrass and farm, so getting an early Chalice of Harmony is always good, then making it into an Athene's Unholy Grail when possible, preferably before late game.
If you want mobility on YOUR side (IE: Not depending on slowing others)) then get Mobility Boots to get into fights faster, if you are actively in fights a lot, and just need mobility to dodge, then I'm sorry but you'll need to rely on Sorcerer's Shoes with either Alacrity or, if you're pushed hard, Homeguard.
I've been playing tons of Vel'Koz, and this is just my opinion.
sorry, mate, Rylai's Crystal Scepter's slow DOES NOT STACK at all, the thing is, both of them applies, but the higher slow commands, and if the duration is lower the other continues acting, I.E. VK's Q has 70% slow, so it applies fist, lets assume it is ont its first rank, so it lasts 1s, the remaining 0,5s (since Rylai's lasts 1,5s) the target has 15% slow (since his Q counts as a AOE spell, not a single targeted). For improving VK's escape you should get Twin Shadows, Frost Queen's Claim (if you are a support) 40% cdr and max your Q for a good kiting. this way I kited both a Jax and a Mundo by myself. rylai's great stats for VK is the health, since it is very squishy
Take ionian boots with alracity enchant, and rylais crystal scepter because your w has no cast time so you can cast it without stopping (and the fact that it has 2 casts makes it very useful for this), and apply a slow to anyone chasing. i got chased across map by a rengar and lived because of this, hitting the q and hitting the e is also essential though haha
Personally, I might grab a Rylai's, an Abyssal Scepter, possibly a Zhonya's, or an Athene's for CDR and mana. Having not played Vel'Koz, not sure what his mana problems are like.
Boots of Mobility. Wait a minute.. Seriously though, i got the impression that the point of Vel'koz was that he was not mobile. Seems to be defeating the point a bit . Apart from that, would you not make him a little bit more resilient rather than more mobile? That seems to fit his style more.
I personally use Sorcerer's Shoe's with Alicrity, as well as either Lich Bane, or Trinity Force. Benefits well from either of those options. Check out my Vel'Koz guide for more in-depth information.
Rylai's Crystal Scepter is very good on Vel'Koz, especially since ( Correct me if I'm wrong ), the slows stack on your Q.
Then get Liandry's Torment and you'll be dealing tons of damage ALONG with your slow and, on top of that, your ult refreshes the procs of both Rylai's Crystal Scepter and Liandry's Torment.
If you want mobility on YOUR side (IE: Not depending on slowing others)) then get Mobility Boots to get into fights faster, if you are actively in fights a lot, and just need mobility to dodge, then I'm sorry but you'll need to rely on Sorcerer's Shoes with either Alacrity or, if you're pushed hard, Homeguard.
I've been playing tons of Vel'Koz, and this is just my opinion.