Against Froslass. Both should be able to take it out easily due to its fire weakness, but it’s usually faster than both so it’ll probably get in a hit. I would go with Flare Blitz Arcanine because it’s slightly more defensive and should easily ohko Froslass. You should make sure that you aren’t trolled into destiny bond or faint from recoil, but if you don’t, the battle won’t be too bad. Then again, Houndoom with flamethrower should do the job.
Against Politoed, a solar beam Houndoom could possibly ohko politoed, it would require setup of sunny day it would be so much more effective than Arcanine, especially because Arcanines best options are Double Edge (could cause fainting tho. Or thunder fang (65 base power, unless you wanna play with RNG and get that paralysis).
Both would be suicide against Kindgra. Kindgra has 2 weaknesses, one that none of the 2 fire types can learn a move of, another that doesn’t exist in HGSS. Whatever you do is death to your dog types, however here I think Solar Beam Houndoom or Dark Pulse Houndoom is the best idea here. You can try setting up Houndoom a nasty plot if you have a chance, that may change the tide of the battle.
I would suggest
252 Speed/252 Special attack/ 6HP
You can switch Sunny Day for Nasty plot if you think you will have a chance to set up or charge your solar beam safely.