Rylai's Crystal Scepter is kinda unnecessary with this build, especially since you seem to really focus AD. Skarner's Q ( Shattered Earth) and E ( Ixtal's Impact) are his main sources of Magic damage. Skarner's Q already has an AoE slow much greater than Rylai's 15% for AoE and his E is a slow particle with a fairly short range that's easy to dodge. It too is an AoE so the only way you're going to get the 35% slow from Rylai's is with your ult which isn't too spammy (to say the least).

If you want health and a slow, a Frozen Mallet would be far better. It applies a 40% slow per melee hit (which, since you're AD, you'll be doing a lot) and gives you more health and attack damage, all for only 100 gold more.

If you don't want a Frozen Mallet, I'd suggest a Rod of Ages instead of a Rylai's. When fully charged it gives you more health, the same AP, and a hefty amount of mana not to mention the in-lane sustainability from Catalyst the Protector. This would help solve both Skarner's relatively weak laning and his mana issues.

almost everytime you kill a champ (maybe 2) you have to go back to base, and miss out minion farming, you have to use almost all your mana to kill a champ.
You miss some armor too, if the enemy team has xin zhao or tryndamere, you're ****ed. You can't run, and you can't damage them enough.

getting rylai's and trinity force is kinda redundant. Both items slow. Not to mention that if you are seriously thinking that you will be getting this kind of build in a reasonable amount of time then that's just insane.

i would recommend getting a sheen after boots because since you can spam q the proc will be up alot