For the purpose this skill serves, currently I just leave it at rank I the whole game to cut down on mana consumption, which I find is better spent elsewhere. Am I doing it wrong?

no

after maxing Missile Barrage you should be maxing Phospherous Bomb, especially during laning phase. The mana costs may increase but it also gives you a lot of burst and has a relatively short cooldown. You should only really be using Phosperous Bomb against a champion when you're going for heavy harass, multiple target damage, or a kill. You can use it to rapidly push a minion wave but it shouldn't be reflex to constantly use it.

i guess it really depend son your playstyle. faster cd jump? or more burst?

Pre-6 I use phos for bush-checks in matchups I can afford to get close enough to bushes to risk it, and to vision enemies that like to try and harass from bushes.

Post 6 I use it for the same pre-6 purposes but also as part of my kill setup not for any kind of damage, but to assure vision for rockets as they flee. Since I get an extra rocket's worth of mana out of having phos-bomb at level 1 this seems reasonable to me.

I level valkyrie first beceause valkyrie's mana cost doesn't increase, I want to be able to engage again after using valkyrie as quickly as possible assuming I'm still in servicable condition. Overall, I find that jump is better for producing a good burst of damage anyhow since it lets me more reliably hit with gatling and auto attacks.

I never use phos-bomb to push minions. Gatling is way more effective if I have to push using abilities, and worth the 20 extra mana.

hoho dont engage with valkyrie. unless it's like a last kill for sure safe environment.
It's your getaway

I use valkyrie to engage only if I'm certain of a kill. It really helps rack up the stacks on gatling, which when two other allies are on the target ensures a quick kill, often before a player can react to flash or use another escape.

Otherwise, yes its a pretty bad practice.

Given the attack range on his autoattacks and gatling gun, its still important to use sometimes for getting a couple of extra harrassment attacks in, then use valkyrie to retreat.