Assuming it was only blocking one creature, it no longer has any creature to which to assign and deal damage, so it doesn't do either of those things.
The Combat phase progresses as follows:
- [CR 509] Declare Blockers Step:
- [CR 509.1] Defender declares blockers.
- [CR 509.2] Attacker declares damage assignment order.
- [CR 509.3] Defender declares damage assignment order.
- [CR 509.5] Players get priority.
- [CR 510] Combat Damage Step:
- [CR 510.1] Attacker assigns combat damage.
- [CR 510.2] Damage is dealt
- [CR 510.4] Players get priority
Celestial Flare is cast and resolves in 2.4. The next thing that happens is the Combat Damage Step. The blocking creature has nothing to which to assign damage, so it won't, so it won't deal any damage.
510.1c A blocked creature assigns its combat damage to the creatures blocking it. If no creatures are currently blocking it (if, for example, they were destroyed or removed from combat), it assigns no combat damage. [...]
510.1d A blocking creature assigns combat damage to the creatures it’s blocking. If it isn’t currently blocking any creatures (if, for example, they were destroyed or removed from combat), it assigns no combat damage. [...]