Can you explain the make up air issue? I always though higher CFM was better for venting .

The OP is referring to the requirement for formal make-up air for flow rates of 400 CFM or above that derives from the International Building Code via the International Residential Code and thence flowed down into local building codes (not universally). It is fair to say that 'enough' CFM is better than 'insufficient' CFM.

In any case, there is always make-up air (MUA). It exactly equals the flow rate achieved by the hood blower. This can be near zero with a tight house, so the hood won't do much, but any combustion appliances connected to kitchen air are at risk of back-drafting carbon monoxide. The crude assumption of the IBC is that all houses of any size are sufficiently leaky that back-drafting isn't a risk below 400 CFM (blower rating).

Depending on the presence and type of such appliances, where they get their air, and how much actual CFM is needed for a given cooking condition under a given hood size, the MUA 'system' may be complex or simple. The OP has to explain a lot more before recommendations can be made.

Kaseki- are you saying that it's best to have a MUA system even if the vent hood is under 400 cfm?

I'll have a 30" induction range, a direct vent gas fireplace in an adjacent room (open concept) and exhaust fans in laundry and bathrooms. Old kitchen has microwave over gas range so not the best situation.

I've read about vents and MUA and I'm still lost on what to do. GC hasn't been helpful. Maybe I should contact an HVAC professional on my own?

I don't know the internal pressure difference with the outside that could back-draft your gas fireplace. It may have its own MUA and hence operate fairly normally no matter what you do in the kitchen. But this is something I would at least ask the supplier of the gas for the fireplace, or the manufacturer of the fireplace.

When we write of an MUA system, we include simply having a duct path into the house with a damper and maybe a filter that will allow air in if the pressure in the house falls due to hood operation. This can be fairly simple, and a HVAC professional should be able to deal with MUA issues. With two bathroom fans, you may already have a 100 CFM of air flowing outward before the kitchen is addressed. How leaky is your house, qualitatively?

Without further information other than "34 inches" I can't advise on what the kitchen hood CFM should be to keep smoke and grease out of the house. The hood should overlap the cooktop side-to-side and front-to-back. The area of this hood entry aperture (sq. ft.) has to have an air velocity (on full power) that ensures that the cooking plumes that are captured by the hood aperture stay captured, i.e., contained. For hot cooking (wok cooking or searing), 90 CFM/sq. ft. will be sufficient. Possibly with tame induction cooktop cooking, as low as 60 CFM/sq.ft. can be sufficient. Multiplying hood entry area by one of these values, and boosting the result by a factor of 1.5, yields the rated blower CFM that you should strive for.

In other words, we start with requirements and then find hoods or hood inserts that meet them. This is inexact, but usually sufficient.

Once the hood blower performance is determined, and the fireplace requirement is known, then you choose the MUA scheme needed. You have no gas hot water heater?

Other factors such as noise requirements are personal issues, but they can further drive component selection.

Once upon a time cooking was performed on wood or coal ovens in kitchens with no exhaust ventilation, other than a chimney for the stove heat source effluent. Today, a decent regard for keeping the interior air clean of cooking odor and minimizing grease deposition, particularly in open concept architectures, demands adequate ventilation of the cooking effluent, even as the cooking heat source becomes locally pollution free.