I would say that this is highly dangerous. It is against US and Canadian code to not have outside ventilation for any fuel-burning appliance in your home; that's your furnace, HWH and stove/oven, assuming all are NG or propane. It is only acceptable to have a "filter-only" vent hood for your stove if it's all-electric (which BTW is the case for every single apartment I've ever rented; gas appliances may be cheaper on utility bills in the US, but a gas stove is a huge fire hazard and general liability for any landlord).
The code is in place for a very good reason; not only can inefficient burning of fossil fuels produce carbon monoxide and smoke (both of which continue to cause damage long after you've reached fresh air), but even when these fuels burn ideally, they remove oxygen from the air and replace it with CO2. CO2 in itself is not toxic in the same way CO and soot smoke are; as soon as you reach fresh air the symptoms of CO2 asphyxia begin to dissipate, while soot and CO poisoning ("smoke inhalation") can kill you hours after you reach fresh air. However, the consumption of oxygen and production of CO2 in a space with inadequate ventilation is a double-whammy for anyone in the same space; the oxygen is being consumed so there's less of it even in upper strata of the room's air, and as the CO2 builds it settles downward in a "blanket", pushing oxygen up towards the ceiling and away from you.
As the CO2 level builds, your body's natural "inhale/exhale" reflexes go haywire in a Catch-22 condition called hypercapnia; your natural breathing while in a high-CO2 atmosphere actually increases the CO2 levels in your blood, but the only thing your body can do to reduce CO2 levels is breathe. So, you start hyperventilating, which only exacerbates the problem. Should you pass out from lack of oxygen, you will not wake up if someone else doesn't get you out of the room or get some ventilation of fresh air through it.
Your landlord is running illegal housing. However, he may not know it, so be nice at first. Follow standard procedure for maintenance requests, and ask the landlord to install a proper outside vent line for this fume hood. If he refuses or drags his feet, you can call in the city's Code Compliance officials, or federal HUD (Housing and Urban Development) representative, and they will MAKE the landlord comply. Depending on the terms of your contract, the landlord may be giving you a free out by not living up to his end, meaning you may be able to break the lease at no cost if this has gone on for some time with the landlord's knowledge and inaction.
Understand that the cheapest way for your landlord to fix the problem with tenants still occupying the units may well be to cap off the gas feed and replace all the gas cooktops with the cheapest electric setups he can find. If this was the reason you moved in, and you don't get a "free out" from this debacle, you may find yourself stuck with a spiral-coil POS.
Best Answer
I'm not sure exactly where this pipe is, or how far back the pipe runs. Though most codes now call for a shutoff valve be installed for each appliance, in the same room and within 6' of the appliance. I'm going to assume that the piece of pipe you're looking to replace, runs from the shutoff valve to the appliance (this might be a terrible assumption, but you didn't supply much detail about your situation). If this is the case, you could use a piece of flexible copper pipe exactly the same size as the one you're replacing. Or you could use a corrugated stainless steel tubing (CSST).
As you've seen, flexible copper is prone to kinking, especially if you're moving the stove often. The CSST is more resilient to movement, and is typically easier for DIYers and homeowners to work with. If you do switch to CSST, you might find that you need an adapter to connect it to the valve. You should be able to find CSST fittings in various lengths, at your local hardware store.
If you choose to replace the pipe with flexible copper, you should shut off the gas and take the pipe with you to the store. With the pipe in hand, it should be no problem finding replacement pipe. You might also find that the end(s) of your copper pipe are flared. If they are, you'll also need to flare the ends of the new pipe. Some stores can do this for you. If they can't, you'll need a special tool to do it.
Without actually seeing the installation, it's difficult to provide any more specific information.