Basically this would depend on how much your students hated you and what background you came from.

Immediate danger? Keep in mind that (as far as I know) the people beating teachers up are not the police or soldiers, but rather radicalized students called red guards. So it's not really the case that the secret police would show up in the middle of the night to make you disappear. And for the most part students were interested in humiliating rather than outright killing teachers.

But events occurred very fast. You would have gotten some idea of what was going to happen due to the increase in propaganda and agitation against school and university administration. The first "Big Character poster" decreeing Beijing University as being controlled by "bourgeois ant-revolutionaries" appeared in May 1966 (written by soon-to-be red guards), and was broadcast/published nationally. There would be followed up by more rhetoric against "bourgeois elements" from official party releases, backing the rhetoric of the red guards. Liu Shaoaqi sent in CCP work teams in June to control the red guards and make sure that they only direct their attacks against "intellectuals" and not apparatus of the Communist party itself. But Mao ordered those teams out, and in August, Mao held a rally of almost a million red guards in Tienanmen square and gave his approval to the movement. The red guards were directed to attack the "4 olds" of Chinese society.

There after the violence by red guards against school administrators, teachers, and members of the Communist party seen as "reactionary" and "capitalist roaders" began. But even at this point it was mostly about humiliation than outright killings. Teachers would be forced to scrub student toilets for example, or forced into making long self-denunciations. Lots of teachers actually ended up committing suicide due to the humiliation. But the violence by red guard kept escalating against both teachers and members of the party, as well as against each other. Rival factions of the red guard fought street battles against each other and in cities with munition factories even acquired tanks for these battles.

By the end of 1966 the government decided that those red guards were too much of a liability, and by 1967 had ordered them to cease their activities. Those who refused to obey were forcibly suppressed by the army. So the whole cycle of the red guard movement took place in around a year.

So basically the answer to your question is that it depended on what sort person you are. If you are the paranoid sort, then you might recognize that sometime between June and August it might be a good time to get out. If you are not liked by your students and under the illusion that the police will protect you (they actually won't) or the students won't persecute you (they probably will), well, then there's a chance that they hate you enough to kill you, or make your life shitty enough you end up killing yourself.

If you are the sort who just kept your head down in the entire post-1949 period, and take care not to have any "counter-revolutionary" material lying around your home, you might actually just get through without a scratch so to speak (this was the story of my maternal grandfather).

Fleeing the country is not a very easy option in mid 1960s China. For one, the government don't just allow you to leave, although thousands did flee from southern China to Hong Kong during this period. Fleeing the city and go living with relatives in another city is an option, but I don't know how easy it was to simply quit your job at the university/school and transfer to another city.

Edit sources:

Turbulent Decade: a History of the Cultural Revolution, Y Jiaqi

Modern China: The Fall and Rise of a Great Power, 1850 to the Present, Jonathan Fenby