What parts, besides the leaves of Thai Basil, are usable? I am making Thai Basil Chicken (Gai Pad Krapow) using the leaves but can I use the stems and flowers as well?
First off, I'm afraid you have been using the wrong type of basil for your dish!
In Thai cooking, three different types are commonly used:
"Thai basil" (or "horapha", โหระพา), which tastes a bit like anise / liquorice; it's slightly purple (as shown in the picture in Jolenealaska's answer).
"Holy basil" (or "kaphrao", กะเพรา), which tastes more like pepper/cloves; it can also be a bit purple, and (unlike Thai basil), it is a bit hairy, and the leaves have jagged edges.
"Lemon basil" (or "maenglak", แมงลัก), which (as the name suggests) tastes a bit like lemon.
Notice that "krapow" is just a slightly different spelled transliteration for holy basil ("kaphrao"). Preparing this well-known dish with Thai basil instead of holy basil will certainly make for a very good tasting dish (I've made it myself a few times when I couldn't get holy basil, and in fact I actually prefer it, since I'm quite a sucker for that anise/liquorice taste), but should really be called "Gai Pad Horapha" instead.
As for your question, I typically use the flowers (of either type of basil) to garnish a dish - if I haven't eaten them already while peeling the leaves off the stems.
I typically discard the stems, but on occasion I have chopped them up and mixed them with some honey and ginger (and some mint, whenever I had it), to be used as a dipping sauce for spring rolls.
The flowers and stems are absolutely edible.
The stems are like cilantro stems in that they have a lot of flavor of the herb but are not as prized for their texture as the leaves. I puree cilantro stems until they are just flavorful, green liquid. That liquid is great in sauces, salsas, soups and dressings. I see no reason why Thai basil would be any different. As a matter of fact, I wish I had some Thai basil right now, I have a couple of Asian pears and some fresh homemade Japanese style mayonnaise. The stem puree would make an awesome dressing for slaw. Also like cilantro, you don't have to puree the stems, you can just chop them up and use them as you do the leaves, it's just a matter of personal preference.
The flowers of Thai basil are a bit more controversial. The flowers certainly are very pretty:
Some people think they are very tasty, others not so much. So on that one, I just recommend that you taste them. If you like them, you can use just like any other edible flower or with the leaves in any application in which you would use the herb.