It would be best to dissolve it in a bucket.

Regarding filters, if you will get 2 or 3 of THESE cartridges, you'll get much better performance, and they will last all season:
Unicel C-4607 Replacement Filter Cartridge (Easy Set Size A or C) @ Amazon
Unicel C-5315 Replacement Filter Cartridge for 15 Square Foot Intex B Filter @ Amazon
The Unicel's filter better than the Intex cartridges, and should last all season. One caution: many online pool company's are shipping non-Unicel cartridges, but showing the Unicel number. Do NOT purchase a a cartridge, if the company lists OTHER brands, except Intex OEM specs. (If Filbur, Pleatco, etc. are listed . . . do NOT buy. Filbur is OK, but what you'll get is almost certainly a Chinese cartridge that's even LOWER quality than the Intex OEM!).

I'll try to get a filter cleaning sticky posted in the Equipment section, today.

I'm not sure (and haven't looked) to see just what filter you have. But you should be able to flush the filter, on most newer Intex pools, by bleeding water out of first one pipe, and then the other, while the filter is open.