I flunked out twice as a undergrad engineering student at a major mid-western university. The second time it was a "go away and don't bother to reapply" situation.
I was determined to be a graduate engineer, my dream since age 10. I went to work as an adult technician at the university to save a few $$. Six months later I started night school as an "adult special", determined to learn everything I had missed during the first two years. For the next year, I basically did every example and every problem over in a special set of notebooks I kept, using the open tutoring office in the old department whenever I had a question. I bought or checked out similar math textbooks to get extra problems to work where I was not perfectly confidant of my ability.
I never got less that an A or A+ (95+) in any class, repeating all the classes that I had received C's or worse in, and met informally with each member of the admissions committee to let them know of my progress. They were encouraging but non-committal. I then re-petitioned for admission to a bachelors upper division degree program and requested that my night school grades by substituted for failing ones. I was readmitted on probation but with the old grades.
I continued on that same track for my junior year - all high A's, all homework triple checked before submission, lots of all-nights, no parties, few weekends.
At the end of that year I was taken off of academic probation. A few months later the department head and the chair of the graduate admissions committee/vice department head separately approached me with an invite visit their labs and discuss their research. I had previously made the acquaintance of some of their other grad students to get an idea of what was happening. Both visits resulted in offers of an RA in a PhD program. So no teaching, just $$ support for my Masters research (optical physics/lasers).
After the Masters thesis I was recruited by a local startup - I made a choice not to go the academic route for a number of reasons. the chance to be in on the ground floor in a new technology, money, a new wife, and a desire to start a family among them.
I was lucky to get a third chance. Good luck to you.