Your most important function as a support is to keep fragile allies safe. Keep Devour's range and cooldown in mind and position accordingly!
Consider carefully when to use Thick Skin's active. Sometimes shielding early to avoid further damage is good, but sometimes the healing is more beneficial.
When you see Tahm Kench use the shield from Thick Skin, remember that he just opted out of a good deal of healing. He will also not accumulate new gray health until Thick Skin comes off cooldown. Use this to your advantage!
If Tahm Kench harasses you by spitting minions at you, try going in for a trade right after he spits. His Devour will be on cooldown and you should be able to trade favourably if he can't eat you.