For some reason, after a solid few hours of searching, nothing about actual escape rates was found. In the comments, it was mentioned that all Pokemon have the same escape rate, which is not true. I'll explain how the factor is calculated for escape.The escape factor is calculated differently in different generations.
At the end of each turn, a random number from 0 to 255 is generated. Then, based on what the Pokemon is doing that turn:
- Eating (Bait thrown): If the number is less than half than the Pokemon's Speed, it will escape.
- Angry (Rock thrown): If the number is less than four times than the Pokemon's Speed, it will escape.
- Nothing: If the number is less than double the Pokemon's Speed, it will escape.
- If a Pokemon's speed stat is higher than 127, it will always escape, regardless of situation.
Source (Generation 1)
No Safari Zone exists.
There is an escape factor. Whenever a wild Pokemon is encountered, the escape factor is set to 3. The escape factor can then be modified by going near the Pokemon or giving it a Pokeblock. At the end of each turn, a number from 0 to 99 is generated. If this number is less than five times the escape factor, the Pokemon flees.
Source (Hoenn Generation 3)
Same as Hoenn, but the escape factor is a Pokemon's unique escape rate, and it is unmodifiable.
Source (Kanto Generation 3)
Pokemon's escape rate is treated as a stat; it can be raised and lowered as stages. All Pokemon keep their escape rate amongst the games of Generation IV, but all Pokemon species have their own unique escape rate. These escape rate chances emulate stat boosts changes (+2 = x2, +4 = x3, etc). A random number is generated from 0 to 255. If the number is less than the modified escape rate, the Pokemon flees.
A curious note about escape rates is mentioned:
>Pokémon at higher evolutionary levels generally have lower escape rates.
Source (Generation 4)
Hopefully that clears up the escape rate situation. However, as said before, after searching extensively, nothing seems to have come up about the actual numbers.
I also checked all of Serebii's safari zone pages; the only percentages that are there are the encounter rates.