An unimaginable number of horseflies swarmed around me.

Literal

Seen [experience-たこともない] [manner-ような] number [genitive-の] horseflies [subject-が], me [to-に] clinging-came [explanatory-のです].

見たこともないような ('the likes of which I'd never seen') combines the experiential negative ~たこともない with ような to modify 数 — 'a number such as I'd never seen.' 虻 (あぶ, horsefly) is a relatively rare kanji — learners would likely encounter this word in kana or katakana (アブ). まとわりつく ('to cling to / swarm around') vividly conveys the insects' persistent attachment. ~てきた adds the directional auxiliary, marking movement toward the speaker. The explanatory のです frames the sentence as recounting a surprising experience.