It's blitz, it may not be morally accepted (to some) but it is legal.
Earlier today I had an OTB tournament. time scramble 25/5d, it was a dead draw [King + pawn + Rook vs King + pawn + Rook] but I avoided 3 fold moves and just kept checking and alternately moving my King. I had 30 seconds left, he had 10. You never know, he might make a mistake. True enough, with 1 second left on his clock, he blundered and I won the rook. I only had 3 seconds left though. so idk if that's considered dirty, but at that point, why not go for it.
Playing Dirty in OTB Blitz

On a similar note, in the first round of an OTB 25|5D tournament a few years back,I am up against a 1200 as a 1500 and we are in a K+R vs K+R endgame. I politely offer a draw and I get declined 3 times. And then my opponent gets skewered and I win the rook; such a turn of events, and both of us were still above 20 minutes………
Well.. that's your opponent's fault. 20 minutes left is not an excuse at all. I'd only accept my situation as something you can play for since we're both literally under 30 seconds left. He was still notating so... his fault too.

So suppose I was in a game and both myself and my opponent had 10 seconds left in a game without increment and were in a time scramble. If I were to intentionally check my opponent (multiple? maybe) times (something that is done often in online chess to undo your opponent’s premoves), and with the intent of calling an illegal move to win the game, especially in a dead draw, would that be considered bad sportsmanship?
There is absolutely nothing unsportsmanlike about doing that. It's zero increment (and presumably delay) blitz. You can make whatever move you want. Trying to induce your opponent to make an illegal move or to flag is perfectly acceptable.

I don't see a problem. At least in my opinion, nothing is "dirty" in chess other then non over the board stuff such as distracting your opponent.

There is nothing illegal or unsporting about giving spite checks. Unfortunately, they aren't quite as effective OTB as premoves are online, since the opponent can see you physically making the move.
By the way, people should be aware of USCF Rule 14H in rated games played without an increment. R+K vs R+K is an obvious example where one player can usually stop the clock and claim a draw by "insufficient losing chances." FIDE has a similar "by normal means" rule for rapid play finishes. The use of an increment nullifies these draw claims. That's one reason why 3+2 is preferred over 5+0.

Yes, there are so few zero increment OTB tournaments now.
Thank heavens! Zero increment is a beast that deserves to go extinct.

Btw, there are videos of GMs making illegal moves in dead lost positions in blitz in the hope their opponent doesn’t know the proper protocol. The rules differ from USCF to FIDE.
According to the Blitz section of the USCF rule book, rule 7d states that:
“A game is won by a player […]
Who, after an illegal move is completed by the opponent, takes the king (if the king is in check) or claims the win and stops the clock, before the player determines a move and provided the player has sufficient mating material as defined in rule 7c. A player who moves his king adjacent to the opponent’s king and then attempts to claim a win under this rule based on the opponent’s failure to notice the check shall lose the game.”
So suppose I was in a game and both myself and my opponent had 10 seconds left in a game without increment and were in a time scramble. If I were to intentionally check my opponent (multiple? maybe) times (something that is done often in online chess to undo your opponent’s premoves), and with the intent of calling an illegal move to win the game, especially in a dead draw, would that be considered bad sportsmanship?