Here are some suggestions for other soldering gear that will make your life easier:
Dispenser for isopropyl alcohol. Useful for prepping a PCB before soldering and for cleaning off flux after: https://www.amazon.com/Stainless-Dispenser-durAstatic-Density-Polyethylene/dp/B00DK2BGIK
Brushes for cleaning off flux. Cut the bristles short to make them stiffer, and use with the IPA dispenser to get off stubborn flux: https://www.amazon.com/Solder-Plumbing-Handle-Inexpensive-Brushes/dp/B07KKH5N8K
Stickvise PCB holder. We like this so much at work that we almost never use the far more expensive Panavise: https://www.amazon.com/Stickvise-Vise-Standard-Nylon-Jaws/dp/B01LJO45W4
Paste flux. The flux in flux core solder is fine for initially soldering down a part, but what if you need to reflow a joint and don't want to add more solder? Also adding flux to stranded wire before soldering helps the solder wick up the wire better. https://www.amazon.com/MG-Chemicals-milliliters-Pneumatic-Dispensing/dp/B00425FUW2
For future situations, I highly reccomend, buying this: https://www.amazon.com/MG-Chemicals-milliliters-Pneumatic-Dispensing/dp/B00425FUW2?ref_=Oct_BSellerC_10704395011_4&pf_rd_p=d35cdc17-a5b5-5f92-966c-e8649e5eb85d&pf_rd_s=merchandised-search-6&pf_rd_t=101&pf_rd_i=10704395011&pf_rd_m=ATVPDKIKX0DER&pf_rd_r=FT4EK0NPGCKWTQW77PJV&pf_rd_r=FT4EK0NPGCKWTQW77PJV&pf_rd_p=d35cdc17-a5b5-5f92-966c-e8649e5eb85d for $10 Plus this iron for $20 https://www.amazon.com/HAKKO-Soldering-electronic-board-FX511-01/dp/B0072QN66U/ref=sr_1_32?keywords=hakko&qid=1564415393&rnid=16310161&s=hi&sr=1-32
and whatever solder you can find and I swear you will become a soldering expert in no time. It all comes down to having the right flux, everything else is easy if you have the right flux.
Is it this on Amazon?
Need to do a keyboard kit and curious if you’d recommend this.
As other have said don’t use that flux but flux is highly recommended as it makes it easier to make a clean joint. Here is what I use MG Chemicals - 8341-10ML 8341 No... https://www.amazon.com/dp/B00425FUW2?ref=ppx_pop_mob_ap_share
Which board..? If DNA, appropriate wire gauges will be listed in the data sheet.
But generally, 16-12 gauge for the high current stuff & 24-20 gauge for low current stuff.
Unless you have a specific reason for lead free solder, leaded will flow much better: https://www.amazon.com/gp/product/B0149K4JTY/
Would recommend some additional flux also: https://www.amazon.com/gp/product/B00425FUW2/ (clean up with isopropyl alcohol & qtips - even thought it says "no clean")
If soldering yourself, don't forget to use leaded solder (63/37 preferred) and good flux. If you don't yet have an iron, my favorite is the Pinecil, it performs wayyy above it's price point, and can run off of a USB-C laptop charger/Nintendo Switch charger/etc. Oh yeah, and make sure to have a tip cleaner on hand, an oxidized tip is a huuuge pain. May as well pick up one that doubles as an iron holder.
What kind of flux are you using? Agreed that it sounds like way too little heat but bad flux (or no flux) certainly won't help anything.
Good flux: https://www.amazon.com/MG-Chemicals-milliliters-Pneumatic-Dispensing/dp/B00425FUW2
Good hot air station: https://www.injuredgadgets.com/atten-st-862d-hot-air-rework-station-1000w-w-lead-free-hot-air-gun-soldering-station-for-pcb-soldering-repair/