I have a Miele Compatto folding bike and the tire and rim size are currently 20" x 1.50. I find that the tubes don't last very long (at most 15 km) I get a lot of flats. Should I increase the tire width to a 1.75 width or possibly buy better more expensive tubes/tires?
Next time you get a flat, take the tube out but keep track of which is side is left and which is right relative to the bike (and mark it). Inflate the tube, outside of the tire, to about 1.5 or 2x its normal diameter, then immerse it in a basin of water and find the leak.
A leak on the inner diameter indicates a missing/defective rim strip, or a spoke that has been dislodged and is poking the tube. A leak around the valve is likely due to under-inflation or lack of care mounting the tire. Two leaks closely spaced together near one side of the tube is "snakebite" and indicates hitting curbs, etc, while the tire is insufficiently inflated. And of course, a leak from the valve itself is due to a defective valve or one where the core is not tightly screwed in.
You may also find leaks where you damaged the tube during installation -- especially likely if you used screwdrivers to mount the tire.
After you find the leak (and the cause is not obvious), place the tube, with the hole marked, alongside the tire and find the corresponding point in the tire. Check from the inside (both look and feel it with your hand) for any piece of wire or glass or whatever that might be stuck in the tire tread and poking through.
People with folding bikes such as Bromptons and Dahons (your Miele is a Dahonesque bike) often report more tire punctures. The smaller wheel means there's more pressure applied to a small contact area and the wheels have to make more revolutions than on a bigger bike for an equivalent distance. People also often underinflate their tires and/or have the cheaply made original tires.
First make sure your tire pressure is correct -- check your tire sidewalls. Folding bikes often have much higher tire pressure than many regular bicycles. Higher pressure means the wheels are harder, which helps deflect punctures, as well as reducing rolling resistance. If your pressure is too low, it's very easy to get a pinch flat.
For example, my Brompton tires are inflated to 90-100 psi -- which is much higher than standard (non-road) bikes. Your Miele has standard Kenda K-West 20 tires, which are 100psi, I believe. It's hard and tiring to get that high of a psi on a regular hand pump, you might need to use a floor pump.
Second, next time you patch or replace your tube, check to make sure that your don't have any spokes protruding or foreign objects in the tire wall.
Finally, you might consider either using a tire liner, tire goo (like Slime), or a better built tire. I know many of my fellow Brompton users have a lot of flats with the standard tire that quickly disappear when they upgrade to something like a Schwalbe Marathon Plus tire which has an integrated Kevlar lining. Your Kendas are relative cheap (20 euro/dollars) and you might do better with more expensive (50-100 euro/dollar) tires with a kevlar lining.