Either pick Oooze/Totem or...
...soloing as Arcane is a mess.
If you don't have -want to bother- someone to carry you for SL, here's a quick guide (I never did SL on my mage)
I personaly pick Tempest Barrier 2/2 and Mirror Image. Use Prismatic Barrier whenever you can unless it is still up somehow. Use Blink when off-cooldown, it'll give you some time against some bosses and a 6% of your max health shield. Mage soloing is all about kill or be killed and every percent count. In the same vein, cast Prismatic Barrier, wait 25 seconds and *then* pull the mob(s). Ice Block is used to give you some time for your cooldowns, don't sleep on it.
Damage-wise, spam Arcane Blast like it's your life's mission and use Arcane Surge for mana recovery. Arcane Orb can be casted while moving and gives you quick Arcane Charged.
For gear, get ilvl 61 from BFA rares and fill the slots with Heirlooms, you'll only miss a good Waist piece if Horde (dunno for Alliance). Check out @Stim
Then farm Auchindoun's first boss, you can get your waist and finger slots but also a staff. When you'll have at least a WF'ed staff you'll have a much easier time soloing. Overall this boss is both the easiest and the one bringing the most stats (4 slots, including waist for Horde so you don't have to quest/go to Kul'Tiras).
Iron Docks is prolly too hard for Mage's toolkit to solo without Ooze/Totem.
Auchindoun should be doable I suppose, maybe Azzakel is a problem. Try to use your Prismatic Barrier for his DoT and get some bandages and health pots (Heirloom neck shares a CD so beware). Getting the spinal injector is big too. Get some flasks too or at least the +4 primary stat reusable one.
Last advice, don't sleep on Stamina, your survivability toolkit relies on HP%.
Don't think I forgot anything, just don't expect gearing to be easy on Mage (without Ooze/Totem ofc) but damn does it feel good to get that gear this way.
Edit : aaaand I forgot something. Charged Crystal Focus, obtained from getting Depleted Crystal Focus and using 10 Apexis Shards (Outlands version) to "fill" them. The Depleted Crystal Focus drops from mobs near Ogri'la and Bash'ir Landing. The tooltip mentions a heal of over 2000 HP and a 5 min cooldown if I remember well. If it still works it entierly outclasses health potions and heirloom necks (shares cooldown with them too)