マックで軽く昼食をとって、スタバでコーヒーを飲んで、しゃぶしゃぶをしながら飲み会という流れだ。

、、。

The plan is: grab a quick lunch at McDonald's, coffee at Starbucks, then a drinking party with shabu-shabu.

Literal

McDonald's [at-で] lightly lunch [object-を] take, Starbucks [at-で] coffee [object-を] drink, shabu-shabu [object-を] do-[while-ながら] drinking-party [called-という] flow [copula-だ].

A chain of activities linked by て-form. しゃぶしゃぶ is a type of Japanese hot-pot dish (onomatopoeia for the swishing sound of meat in broth). 飲み会 'drinking party' — a workplace/social staple. ~という流れだ 'that's the flow/plan' wraps it all up as a planned sequence.