Adobe is the name of a company (like Google or Microsoft).
I think the you mean Kindle does not have the PRODUCT Adobe Flash.
I am no expert in this area but I believe Flash was heavy on battery use so was bad for tablets.
At one time you could get Flash for Kindle (I believe it was preinstalled) but now Adobe have stopped making Flash available for tablets so Kindle no longer pre install it.
I believe that the latest version of web technology (HTML5) has support for video and this will replace Adobe Flash, but many web sites have not moved across to HTML5 and are still using Adobe Flash for their video.
p.s. The kindle actually uses Android as its operating system (heavily modified) and it is actually Androids support for Flash that is important.
Searches for "Adobe Flash on Kindle" and similar searches gives lots of hits, this one may be useful:
http://www.amazon.com/forum/kindle?_encoding=UTF8&cdForum=Fx1D7SY3BVSESG&cdThread=TxTR71JR4GVXQM