In the TV show (SPOILER ALERT! and this comment is only going to comment on TV!Grant, although I have read the book), Grant’s interactions with Strange fall well within the range of activities that would normally lead to slashy activity in any fandom. He isn’t overly demonstrative, and maintains his English stiff upper lip in an appropriate way, but I don't think you have to be English to pick up the nuances of his behaviour:

Initially suspicious of Strange, he is won over by him (the classic romantic cliché);

After Jeremy's death, he treats Strange rather gently: he tries to reassure him, and even goes as far as giving his arm a pat (still a big deal for the average Englishman);

He is the one who comes looking for Strange when he has been closeted with the Neapolitan soldiers for three days, and tries to help him; when Wellington provokes him, he removes the gun from Strange’s hand very carefully, aware that Strange is right on the edge of losing his shit;

He continues to hang out with Strange in civilian life (viz. the billiards scene in episode 4 sees him drunk and chummy; he describes Strange to another character as "my friend here");

He visits Strange in jail: he offers practical help, advice, tries to reason with him. He obviously cares about him;

(In the deleted scene) he takes part in the exhumation of Arabella's “corpse”, in order to help him, which was not only illegal, but would have been pretty unpleasant, as he had known her when she was alive;

He is demonstrably the closest thing Strange has to a friend in Arabella's absence (whether at war or after her death).

Unlike Sir Walter Pole, who also has a friendly relationship with Strange, Grant doesn't have any additional baggage, so he can interact Strange without any ulterior motives.

I hope this helps inform the reasons why he has become such a popular partner for Strange. Add in the idea of situational homosexuality (i.e. during the war), and the fact that they obviously come from a similar social background, and are both attractive, compassionate, intelligent men in their thirties under the command of the charismatic Wellington, and it's easy to see the appeal of the Grant/Strange thread.