A phone call came in while I was eating dinner.

Literal

Dinner [object-を] eat-[ongoing-ている]-time [at-に] phone [subject-が] hang-[come-toward-てきた].

Two structural points. 食べているときに is a classic 'while' construction: ~ているとき ('the time during which X is happening') with the time-particle に. 電話がかかってくる ('a phone call comes in') is a fixed collocation — かかる ('to hang, to be hung upon') is used for incoming calls (the phone is 'hung' with a call); 電話をかける is its transitive counterpart ('to place a call').