20:11 What does it mean here that heaven and earth fled away from Christ's face and there was found no place for them?

Opinions are divided among bible commentators as to what this means exactly. Some hold that it means that the present heaven and earth at that time will be literally destroyed according to scripture and will cease to exist (cp Isa 34:4; 51:6; He 1:10-11; 2Pe 3:7, 10-12).

Those scriptures do not mean that the present heaven and earth will be literally destroyed and cease to exist, otherwise the following scriptures are meaningless (cp Psa 78:69; 89:2, 28-29, 34; 104:5; 119:89-91; Ec 1:4). The clear teaching in all these scriptures is that the present heaven and earth will always exist; they are eternal.

To properly understand Rev 20:11 we need to carefully examine 2Pe 3:7, 10-12 (cp 2Pe 3:7, 10-12). We learn in V7 that contemporaneous with the great white throne judgment "... against the day of judgment and perdition of ungodly men", heaven will pass away, the elements will melt with fervent heat, and earth and the works it contains will be burnt up.

They will all be "dissolved". Dissolve means to loose, loosen, unbind that which is bound; to dissolve something coherent into parts; to destroy. In the context of 2Pe 3:7, 10-12, it means that heaven and earth will be loosed from their present corrupt state into a new state. They will be purified by fire and made new as to character (cp Isa 65:17; 66:22; He 1:12; 12:27-28; 2 Pe 3:13 with Rev 21:1).

The word new in 2 Pe3:13 and Rev 21:1 used to describe heaven and earth is from the Greek word kainos. It does not mean new in existence, but new in freshness and character (cp 2Cor 5:17; Rev 21:5). Heaven and earth as we know them will be renewed, not destroyed.

Fled away in Rev 20:11 means to flee, to shun, to vanish. It is used here of the flight of physical matter. There was found no place for them simply means that there is no place for them in God's eternal kingdom in their present corrupt state. Elements in 2Pe 3:10 refers to the substance of the material world. The works that are therein include all man-made things that are in bondage to corruption (cp Ro 8:19-21 (see also comments on Ro 8:19-21).