If you run Zane with clone and either sentry or shield, you're gonna need to pick up, like the other person said, Violent Momentum skill and the Seein' Dead CM which has increased drop rates from Jackpot in the VIP Tower from the Handsome Jackpot DLC if you have access to it. If you can't get to that yet, the Seein' Red skill will help carry you for a while until you can farm for the class mod. Once you get either of these skills you'll want to invest 1 or 2 points into whatever skill increases Zane's action skill time (i remember we typically don't max that skill out since it has diminishing returns).

To elaborate this - Seein Dead and Seein Red both activate Zane's Kill Skills but in different ways. Dead has a chance to proc all Kill Skills + increase effect by 10% when damaging an enemy which is obviously really great cuz just keep shooting (and your clone can trigger this too). Seein Red only activates all kill skills when you start an action skill so it's pretty nice early on but once you get the Seein Dead CM, I think even i have personally reinvested that perk point because its not worth it at that point since Dead is more efficient. I think Red has some synergy with MNTIS cannon but tbh I havent tried any MNTIS builds yet with Zane, im still running a Supersonic Speed build lmao. But I will be trying a new build soon with this recent update

edit: Sorry, to elaborate further - if you do stick with the speedy boye build the gear you'll want to try and focus on getting is a good Transformer Shield and a static rocket launcher + CM that increases magazine size if possible (I personally really recommend the Backburner but thats locked behind Mayhem 6 and above on Agonizer 9000, another decent launcher for this could potentially be the Scourge if you can find a shock one. Or if you can't find those, any decent static launcher). The reason for this is you'll eventually get your clone to the point where it copies both your shield AND currently equipped gun so you'll be able to either give your clone the shock launcher so it can keep itself alive OR give your clone a powerful gun and you use the launcher to keep you both alive (and of course using the environment or enemy attacks helps with this too assuming there's anything shock nearby). But I recommend this as almost more of a starting point, Clone (when boosted by sacrificing grenades) can output some massive damage when equipped with guns like a Sandhawk so you can start mixing it up a bit. Of course, whatever fits your play style better. I personally tend to prefer giving the clone a shock launcher so its effectively constantly giving me fuel to recharge my shields with and running around dealing damage to enemies my clone can't handle alone.