It sounds like you might be looking at a similar setup to purge gas for arc welding.
Here you would typically a regulator which screws into the valve fitting of the gas bottle which provides coarse control for flow-rate and also has a pressure gauge so you can see how much gas is left in the bottle. For fine control applications like TIG welding it is also common to add a combined flow meter and valve downstream of the regulator (usually screwed into the regulator outlet) these are typically of a 'peashooter'type in the range of 0-25 litres per minute. In my experience this will allow for straightforward adjustments in the range of +/- 0.5 litre per minute with good consistency.
All of this is manually set but with welding the gas flow is turned on and off by a solenoid valve so you could simply add an off the shelf welder solenoid into the loop and hook it up to your control system.
Note that these solenoid valves can be a bit leaky over time so you may also want a more positive manual isolation valve in the system, although turning off the bottle vale will achieve the same thing . So you preset the flowrate and control the duration of pulses of gas on demand rather than attempt to precisely adjust a constant flow-rate.
This has the advantage that it is all off the shelf and easily available components and the requisite fittings and hoses are readily available through retail outlets. Without knowing your exact requirements it is hard to know if this sort of setup would be ideal but it does have the advantage of being a cheap and convenient way to set up a proof of concept prototype at the least.
One thing to be wary of is that the reactivity of oxygen usually demands that oxygen specific parts (especially hoses, seals and regulators) are used. But if you are using inert gas to fine tune the mixture this shouldn't be a major problem. Oxygen is routinely used in industry and it's not absurdly dangerous but you should certainly familiarise yourself with the risks and proper precautions associated with oxygen specifically and bottled gas in general as some of the hazards are not intuitively obvious.
This also applies to the chamber itself, any seals, adhesives, hoses etc should be rated for exposure to pure oxygen and you may need to employ a check valve to keep oxygen out of your inert gas lines.