I did run D2 and ATMA a few years ago on a Linux box using Red Hat 6.x and WINE but now I am primarily using MacOS instead. Sir Lister runs Diablo and ATMA under Linux currently (Ubantu, maybe?) and I'm sure he'll have some useful advice. If I remember correctly, he had found ATMA to run fine under WINE for moving items, but the drop calculator didn't work under WINE and crashes ATMA.
Indeed, my only d2 problem is the drop calculator in ATMA. Note however, that hot-muling won't work reliably. Sometimes when having ATMA running, I can start the game without it crashing, at other times it does crash, so I tend not to try. If the game is running, and you try to open ATMA, it does tend to crash. (at least one of the two, probably both) This is one of the reasons I try to have updated readouts, so I will be able to check whether I need to keep items or not. As to Flavie: it works (at least the 1.5 beta), but I found double clicking on the jar file did not. Instead, I open a terminal and type (when in the Flavie directory):
java -jar Flavie.jar
(I could make a shortcut for it, have been to lazy for that so far though)
Note that due to the way ATMA is called by Flavie, you can not use the option to create the dumps (nothing will crash, it just won't work and you'll get an error message). I still have to do this, but based on the Flavie-files, it should not be too hard to create a script for it.
Installing Diablo 2, LOD, patches, and ATMA is all done by using something like wine setup.exe (iirc, it's been a while). Since you did mention Ubuntu, do search the Ubuntu gaming subforum for Diablo, and you'll find all the problems people encountered, as well as instructions of how to deal with them. (even if you decide to go with another distribution, it might still be worth it, and be sure to check the forums related to that distribution)
One thing I had was being unable to use alt to pick up things, I'm not sure, but this might depend on the desktopmanager you use, in gnome, I had to change the settings for window preferences not to use alt for moving windows.
In any case, try different graphics settings, I'm using the 2d since that works best, there is however a wrapper to use glide mode in opengl, which should give some performance improvement, I never managed to get it working though, neither in linux nor in windows. Direct3d works quite awful and is not advised, but then, it might be different on your machine.
Textmods do work, but I've not been able to find out how to change the settings to use a different folder for easy switching between different textmods. Append the -direct -txt to the shortcut you make as normal. (you do need to change the standard shortcut created when installing iirc, I don't think installing under wine appends wine) But instead of using a subdirectory, I'm using the runeword mod with the data directory within my Diablo II directory. If you do play a lot of different mods non-simultaneously, I'd advise you to make a shellscript for each of them that deletes the data subdirectory in the Diablo II folder, followed by copying it's own data directory from say Diablo II/runewords to Diablo II and then launching the game. Note that you do need to type Diablo\ II and not Diablo II for the directory.
Never having used the red rune mod, I cannot comment whether it works, but I assume it does, and that if you want to use both that and the runeword mod you have a single shared data directory, which really should be the same technique as for only the runeword mod.
Also, on another matter, before you start doing anything, are you already using Linux in a double boot configuration with windows? If you do, keep it that way, until you're comfortable with the way Diablo works under Wine, it might take you a while until you find the right settings.