I have connected the main sewer outflow from my house to the sewer line of the town which runs outside and at right angles to my house. My individual sewer outflow line stems from a chamber in my backyard to which all the drains from different bathrooms and toilets within the house are connected.
During very heavy rains I find the chamber in my backyard flooded, presumably due to back-flow from the town's main drain, although the chamber is at a slightly higher level than the town drainage line. Can installing a sewer trap between my backyard chamber and the town drain line stop the flow-back?

Trap will not prevent city sewer from back-flowing into your sewer line. You may want to consider Back-Flow Valve and cut it into your sewer before it leaves your property.

Make sure you don't have rain run-off water pipes connected into that "chamber" in your front yard. Those may be gutters and/or site drains.

Quick answer is as Milo said, "simple trap" (intended as "gases" trap only) will not stop town sewer back flow as you suspect is happening. Furthermore, an in-line back flow valve (gravity or spring assisted) will not function properly, being easily clogged, thus inoperable causing your wastewater to not drain to town sewer at all. And cause flooded chamber and yard at all times.
Now for some questions: Did you have town permit and approved design to connect your "chamber" (septic tank without drain field) to their sewer line? Most municipalities require a proper design to avoid your described problem. Also perhaps the chamber (concrete) or your house drains have cracks that allow excessive standing water in yard/soil to enter chamber (so not fault of town's sewer line). Another problem may be that the elevation difference between your chamber discharge pipe and the town sewer is too little for proper function/flow. Typically the town sewer elevation should be many feet (say 5 ft minimum) below your chamber discharge pipe. Municipal sewers are supposed to be designed to not have water levels (between each street manhole) much over one foot above the sewer pipes between each street manholes. If town sewers are in fact surcharging with high internal water levels (common during storm events), this can cause sewage to back up into your house line toward your chamber. If you do not have adequate elevation difference as you indicated, then this may be happening also. Maybe you can check to see if the water levels in the town's downstream street manhole is filled very high during a storm event; then perhaps you can get town to try correcting by cleaning their lines to not surcharge so much. BUT town's problem may not be easily solved for you as individual (i.e. major sewer rehab). So last option that would work is to abandon your gravity drain line to street sewer and install sewage pump in your chamber and discharge via pressure pipe (2in dia HDPE); running pressure pipe shallow until entering steeply dropping below street pavement (? ). This brings us back to Town approval/design to do construction in their street and connect to their sewer? Imagine you do not really want your Town named!

No! You're thinking of a "Running Trap" (see image) and as eddiyand Milo pointed out it will prevent sewer gas from entering your home but not a back up from the street.
What prevents a street backup is a "backflow preventer" (see image).
There are several down sides to this.
1) It's mechanical and can fail. **AND**
2) When the backflow preventer's in a closed position anything you flush or drain will back up in the lowest fixture or fitting in your basement.
As a rule this would be the floor drains. They also make backflow preventers for floor drains,(see image) so you could hold a flush or two
Until it reaches the lowest fixture installed.
Good luck, Tom

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