The grammatically correct rendering of this phrase is ‘time flies’. The verb here is ‘to fly’. And, in the third person singular in the present, this verb becomes ‘flies’.
It is a third person because ‘time’ is an object or an ‘it’. In the English language, the third person singular is attached to the pronouns he, she and it. In the third person plural, it is attached the the pronoun they.
It is singular because time is singular. When we imagine time, we imagine a single phenomenon. Sometimes, indeed, time is personified as a single allegorical being.
It is in the present because the phrase is in the present. Here, as often, the present tense in English is used to convey a sense of a general truth: Time, in general, flies.
So, ‘flys’ is incorrect. The word ‘flys’ does not exist in the English language. It may be said that the phrase ‘time flys’ is orthographically rather than grammatically incorrect.