"Thanks for the link! I'm assuming it's ok to make the mixture in both glass or plastic bottles?" Glass is best if you have it, otherwise check the type of plastic in a plastics compatibility chart online for sodium chlorite, HCL and DMSO.
You can look at
this compatibility chart
and find that DMSO & silicone rubber is rated 2, fair. Since the DMSO in the silicone bag is very diluted and won't be in the bag very long, I would not be concerned.
Note the chart legend: 1 = Satisfactory, 2 = Fair, 3 = Doubtful, 4 = Unsatisfactory, X = Insufficient Data
The fair (2) rating is just below the highest rating of 1.