While finding a job that offers both security and flexibility can and will prove extremely challenging, it's not impossible. There are many jobs out there that can offer the best of both worlds. There are telecommute positions which can give you both. There are many freelance jobs that can offer both. You just have to spend a little extra time when searching.
This is the corporate argument that corporations are better for workers. Large corporations allow for lateral advancement as well as vertical. Job flexibility within a large corporation exists within lateral changes. A person can move to a different location with different responsibilities within the same company. The person can then be assured he will have a position with a company he has been loyal to while also exploring new positions within that company.
I think that there are jobs out there that can offer both flexibility and security. But they are really difficult to find. In the traditional work field, it is probably difficult to find such a job. But with the creative field, there seems to be more of an atmosphere that these two factors can co-exist.
Yes, job security and job flexibility can co-exist, because there is often less pressure on each party. A person who has the flexibility to live their life also has the motivation to want to hang on to the job. Job security is a matter of commitment from an employer. Security does not mean they can take advantage of employees by being rigid.
Yes, it is possible for flexibility and security to exist, even within the same company. This requires a lot of communication between management and staff, and it requires a willingness on the part of management to make moves when necessary and allow staff members to grow. Some organizations cannot handle it, but workplaces like Google show the benefits of flexibility.