I don't know how Flash downloader works, but presumably it would only affect Flash content...

There are two different preferences you need to change on Android (compared with only one on desktop). Here are the steps:

First, you need to know the folder path you want to use. An app like ES File Explorer File Manager will be helpful if you do not have a file manager.

(1) Open a new tab to about:config (type about:config in the Awesomebar and tap the go arrow or tap Enter).

You may want to bookmark this for easier future access.

(2) In the search box, type down and tap Enter

(3) Scroll down to browser.download.folderList and tap Modify, then change the value from 1 to 2 (from "default always" to "last used folder"). The change should appear after a few seconds.

(3) Scroll back up and tap the large "+" button to the left of the search box to add a new setting

(A) The name of the preference should be browser.download.dir (this stores the last used directory)

(B) On the right side, tap Boolean and in the popup change it to String

(C) The value depends on the folder you want. For example:

/sdcard/FxDown 

(D) Then click Create (if you are too slow, it may clear and you might have to start again)

If you switch back to your other tab and download something, it should go to the new folder.

Any improvement?

It looks as though I correctly changed the file path for browser.download.dir before. Jpeg file will go to external SD card, but a video file, after downloading through Firefox 33 with the flash downloader addon, goes to internal memory everytime.

Sometimes you can modify options for an add-on through the menu (Tools > Add-ons, then tap the add-on). If not, you probably need to contact the add-on publisher for a workaround or for a fix in the next release. Often there is a support link for an add-on on its page on the Add-ons site.