Cross-training is well-established as a way to improve your dancing. Skills acquired in one dance often complement those acquired in your first. Folks who start out lindy hopping bring those skills with them to blues dancing and most of the time this helps them advance quickly through beginning and intermediate blues courses. However, some key features of lindy hop can be counter-productive to "looking like a blues dancer".
A brief aside: when it comes to social blues dancing, I believe there are only two important rules. 1. Blues dancing comes from Blues music -- honor the music with your movement. 2. Be attentive to your partner. Whatever training you choose to do, whatever extent you wish to pursue, as long as you keep those two things in mind...you'll have fun dance after fun dance. And that's a pretty wonderful thing! But, if you choose to do blues dancing competitively, you'll want to study the blues aesthetic.
I want to emphasize that the view points here are coming from someone who has studied both lindy hop and blues dancing extensively, and loves both of these dances equally; I don't think either is "better." When I talk about looking like a blues dancer, I mean choosing to dance within the blues aesthetic, and making artistic choices that reflect the shared understanding of "what blues looks like" that exists in the wider blues community. This might seem cruel or almost counter productive, but I'm actually going to leave talking about what I think constitutes the blues aesthetic to a future post. What I'm going to talk about here is some very specific characteristic choices that, when combined or used for the majority of a dance, will provide something that has a bit of the "look like lindy hop" vibe to them.
1. Continued use of stretch and release dynamics
Stretch and release is a prevalent description in lindy hop for the dynamics that exist in the swing out. Tension is built up as partners stretch away from each other, and then released into movement. This feeling is super friggin' satisfying, and exists nearly all of the time in lindy hop. But it's not typical when applied throughout a blues dance. While stretch makes appearances from time to time, the majority of one's time in blues dancing is a more neutral connection. Note that this is one of the reasons that some folks will say that there are no rock-steps in blues dancing: rock-steps frequently generate the stretch part of the stretch release.
2. Frequent use of linear momentum
Despite having a fundamental move called the lindy circle, lindy hop frequently uses patterns that rely on linear momentum. This is a bit of an extension and rephrase of the first point, but even without stretch-release as the generator, too much linear momentum will give a lindy hop flavor to your blues.
3. Moving the body as a single unit
There's a preference in lindy hop to move all of the body at once - that is to say, without isolating any part of the body. This intrabody connection is super rad and helps make leading and following at fast speeds easier. While it's true that blues isn't always slow (see Struttin', some Shuffle Blues, some Latin Blues), the more neutral connection and lower BPM range allow more time and opportunity for interesting body isolations such as hip hits, shoulder rolls, shimmies, shakes, and torso movements. Torso isolations are particularly rare in lindy hop, and bringing them back in from your blues to your lindy hop can have really bizarre and interesting effects.
4. More time in open position
A swing out is about 75% open position (depending on whether you count 5 as already open or not) and 25% closed position. A circle is 100% closed position. Side-by-side Charleston is in promenade. But generally, most movements in lindy hop are in open, with a side of closed for good measure. The current trend in blues dancing is towards close embrace connection, with a good chunk of closed, and a side of open and break away for flavor. Seeking this balance can make a large difference in how your dance is perceived.
Any and all of these choices could be perfectly valid and even artistically exciting choices for expressing the music in a social setting, or even in a competition setting!
No one, least of all me, is suggesting that you spend all of your time in close embrace, shimmying while neither compressing nor stretching, forever, the end. But awareness of these qualities of your partnered dancing can certainly help you to enact blues in a way that will look and feel more like blues dancing. I highly recommend taking a private lesson with an instructor if you're ever uncertain about what characteristics a different instructor might perceive as "looks like lindy hop." We love helping dancers find their best dance, and part of that is helping them do the dance they think they're doing!