Are tubeless tires the solution to frequent flat tires?
I wouldn't go for tubeless as a first attempt to solve the problem.  Tubeless might be a good solution for skinny racing bike tyres, which are rather prone to puncturing.  But you really shouldn't be having much of a problem with punctures on a hybrid bike with 32C tyres.


Tubeless usually requires new tyres.  If you're going to buy new tyres, there are plenty of options such as kevlar-lined tyres that are very puncture-resistant. (Schwalbe make various kinds such as Marathon that are well spoken of by cyclists in much rougher environments than the road; other brands are available.)
You might want to consider tyre liners as a first line of defence.
Honestly, that many punctures in such a short time suggests that you're doing something wrong.


Are you making sure that whatever caused your puncture has been removed from the tyre before you fit a new or repaired inner tube?
What do the punctures look like? If it's on the inside of the tube, it's a problem with a spoke. If it's two separate holes on the sidewall (a "snake bite" or "pinch" puncture), it's because you hit a kerb or pothole too hard with under-inflated tyres and pinched the tube between the rim and the road. If it's a single hole on the outside, you ran over something sharp. If it's at the valve, either the valve hole in the rim has sharp edges or you didn't install the tube properly (the valve should be at right-angles to the rim, for example).
An unfortunate feature of cycle lanes is that road debris naturally migrates to the side of the road, where the cycle lane is. Cycle at least a couple of feet from the kerb to avoid the worst of it.
Avoid potholes as far as possible; ditto drain covers, manholes, etc. Make sure you always know what's behind you so you know when you can cycle around them. If you can't avoid a pothole, lift your bottom slightly off the saddle and cushion the impact by letting your knees flex.  Avoid puddles wherever possible&nbsp;&ndash; you don't know what hazards are under the water.
Speed bumps are just potholes in reverse so be careful there, too.  A common arrangement in the UK is to have the cycle lane bypass the speed bump, with a raised kerb between the cycle lane and speed bump, to force vehicles over the bump.  The kerb means that street sweepers can't get to the cycle lane so, again, it fills with puncture-causing debris.
Make sure you're running your tyres at the correct pressure.  Too soft and you'll get pinch flats; too high and minor damage can turn into a flat.



Also, you should definitely consider repairing your inner tubes. It's easy, saves a lot of money and the repaired tube is just as strong as the original. Also, it helps you diagnose the problem, as discussed above.