I am about to start running a Lost Mine of Phandelver group and I am wondering if I would get any experience credit from running it. If so, how much would it be?
As of Season 6, the rules for allocating DM experience have changed. The rules in the AL Dungeon Master's Guide (contained in the D&D Adventurers League DM Pack) trump all previous guidance, including that contained within the individual products.
The new system is based on runtime and average party level. For modules, use the published runtime and published average party level. For hardcovers, use the actual runtime and the actual average party level.
The same package includes a content catalog, listing all the available hardcovers and modules. Despite the packaging, Lost Mine of Phandelver counts as a hardcover.
A DM gets (300 XP + 150 gp) x (tier of play) per episode, where the tiers of play are as defined on PHB p.15. Note that episode is not a play-session: it's a "part or chapter" of the published adventure.
You can find this rule in Section 2 of the Adventurer's League Player's Guide; it's p.13 in the season 3 version linked.