Will purchasing the 'Elite Dangerous: Horizons' DLC from Steam cause conflicts?

No, there is no conflict. On Steam, the actual "Elite: Dangerous" title consists of a launcher that is tied to your Frontier account. The launcher and Frontier account is what gives you access to the DLC, not Steam. Steam is effectively optional here, since the launcher is where all the magic happens.

The base game you download from Steam includes the Horizons content already, inputting the key you get from Frontier or the Steam store merely unlocks it.

Regardless of where you purchase your key, as long as it's tied to the same Frontier account at the end of the day, it will work in Steam.

Generally, when you redeem a key on Steam, Steam treats it is as if you had purchased that game on Steam with money. When another store offers you a steam key, and taking that offer doesn't invalidate your ownership on that store, then you will own the game twice. Once on the original store and once on Steam.

Also note Steam's refund policy. When you bought a DLC package which doesn't work, you can refund it within 14 days, unless you played the base game for more than 2 hours after purchase.