I'm really curious to know what kind of America he wants to build. I come from a military family, I like veterans. If I owned a business I would employ the freak out of vets.
I don't understand the logic of trying to make them teachers.
The least cynical reading that I can come up with is to give recently retired/separated veterans or their spouses (of which there are likely a large amount in Florida) a chance to immediately get into the workforce rather than having to attend grad school first to obtain a teaching certificate. A lot of vets, just due to the nature of their training, are pretty much one teaching certificate away from qualifying as physical education teachers.
Reading between the lines, the recent Don't Say Gay legislation and state level meddling and restrictions on curriculum could have convinced a not insignificant amount of teachers already combating low pay, intrusive parents, long hours, and having to pay for many of their own classroom supplies that the field is just not worth it anymore and this provides the state with a new source to fill in the gaps.