There are companies from which you can order bespoke mRNAs. Lead times vary but are in the weeks. Many are abroad. The other components of mRNA vaccines can be assembled by someone with 2 years of biochemical Ph.D. experience. There are no laws against a person assembling and injecting themselves with anything.
I have extra sympathy for the writer of this article, since mRNA vaccines (even if they were a random sequence) are relatively lower risk than many other sorts cancer interventions which are FDA approved. I happen to be an ex-professor, who is a director at a drug company. I know that if I were the unfortunate author of this article, whose heart is in the right place. I would probably be injecting myself with my own janky version of whatever offered hope.
Whether that would actually change my prognosis? Probably not. I can say though that I _would_ and I believe others are entitled to positive freedoms I'd afford myself.