For better results it more important to use thermal paste in between aluminium rectangle pipe and peltier. With this aluminium will keep the peltier at room temperature.

Your aluminium rectangle pipe should be like a heat sink. This will also keep the peltier at room temperature all the time.

If you have Strawhat 8mm 0.25W LED its ok. Actually I find 1W special LED has better results not every 1W LED. If you find this 1W LED then take other strawhat LED is ok. Every 1W LED has a yellow colour dot in its centre. Always take that 1W LED that has very small yellow colour dot. You can see in the picture yellow dot. The   LEDs having mark are ok and having cross are not ok. 

Strawhat LED is also best and easy available  if you can not find 1 Watt LED with small yellow dot. here is the link  where we I have bought

http://projectpoint.in/index.php?route=product/product&product_id=500188647086

Heat sink should have more legs and light weight. Here are pictures of heat sink first have no legs and little heavy and second is light and have more legs

If we compare human hand and head then head is the best for    heating the flashlight and our hands remain free for doing any kind of work like studying or going at night in dark. where your sight would be there would be light.

If you have no knowledge of electronic no problem. I will sagest  you a circuit take from txl group below is the link where you can buy the circuit. it has two sides one is its input side +ive and --ive signs  where our  one peltier has two wires +ive red wire and --ive black wire we will connect with soldering +ive wire on +ive side     and --ive wire on --ive side. And the other side of the circuit is      output side it also have +ive and --ive sides. Now our LED also     has +ive and --ive signs. So we will connect the LED with soldering +ive with +ive  side of circuit and --ive with --ive side of circuit.

circuit link  

  https://customthermoelectric.com/elc-vb0410-1-unipolar-voltage-booster-40mv.html

When I start creating flashlight. I took few Peltier’s their output volts were about 40mv. I tried my joul thief but failed many times they were not able to convert from 20mv or 40mv. There was a lot of search on internet any help about low volt conversion. After a lot of search internet I found two solutions about. Both were right for me. First was a IC that called LTC3108 available at analogy devices. Specially made for thermometric harvesting  devices like Peltier’s . That is available at many website like ebay.com or any that suite you. It has select able option about volts 2.5V, 3V, 3.7V, 4.5V or 5V. Here is method that you can make you own boosting circuit.

Components that you need

Fallow the pictures to make your own ultra low volts boosting circuit that start form 20mv  

Thermometric generator peltiers are easily available in market. even in  price of .5 usd from china. But in accidental fall their efficiency be comes down. So do not buy like these peltiers.

So I suggest  any athantic online electronic store. Which you like. Here is a electronic store link where you can choose the peltier according to your design. But you can choose any store which you think easy accessible . 

https://www.digikey.com/products/en/fans-thermal-management/thermal-thermoelectric-peltier-modules/222?k=peltier

When you have more than one peltier so I suggest to make their series. For making series of peltiers simply connect one of +ive side with other peltier --ive side. As increasing peltiers you can increase the +ive with connecting --ive side. Below is the picture of series. First and last remaining wire will be connected with our volt boosting circuit.