I preferred flashcards as well & as a matter of fact, K didn't like TV or computer programs as well & didn't seem to learn as quickly from them. We used laminated card stock flashcards until she was about 3.5 years old when we finally made the transition to using Little Reader as a computer program only. In fact, until K was 3 years old, we included a picture on the back of almost every flashcard because she did not like word only flashcards. The odd one we didn't do this with, but usually that was because it was difficult to describe with a picture. After age 3, this was harder as we started doing the Dolch words like and, it, the, which can't be portrayed with a picture. Laminated flashcards with pictures took lots of time as well as used a lot of ink & time & money for lamination, but I really think that it was the most beneficial way to teach my daughter. It will not be the same for all kids, but for K it was because:
1. printed, laminated cards with pictures kept her interest better which is the most important part of teaching a child
2. by including a picture with each word, K developed an understanding of the meaning of each word & I feel that she has excellent comprehension for her age.
When just beginning, I recommend starting with familiar & fun words. Thing like family member & pet names, lots of nouns & fun action words. If you like Little Reader after the free trial, make sure you check out this link to learn about their discount for kids with DS, etc. If you choose to print & laminate cards there will be a cost involved in that, but at least the initial program with it's thousands of files & pictures will be free which will save you tons of time.
If you do choose to use printed flashcards rather than the computer program, I highly recommend laminating them. I have written about several different ways to laminate in this post.
Make sure you fast flash them like in this post.
I would teach both kids at the same time. These methods are meant for really little kids, even under age 2, so I'm sure you will have great success with both kids.
3) Is the Doman book recommended even IF you are using a reading program, such as Brill Kids, or does it basically just teach you what the packaged programs is already implementing? Or vice versa!
You can use one of the reading programs to do basically the same thing, but personally, I would still read How To Teach Your Baby to Read, or even the reading section in the How to Multiply Your Baby's Intelligence book. It really helped me to have an understanding of why the method worked & when I understand things better, I can implement the idea better.
The simplest thing would be to use a video program like Your Baby Can Read or get the BrillKids Little Reader & use their semesters one & two on the computer. The next best & still pretty simple is to still follow the Little Reader semesters, print them out & show them by hand. If you use the fast flashing method that I talked about above, it will require only several minutes a day to show the cards to both kids.
You are very welcome!