There’s a difference between “asthmatic” (asthma) and “basmatic” (basmati rice), but there have been jokes. This was printed in the Sunday Mail (Glasgow, Scotland) on August 26, 2007, reporting on the best jokes from the Edinburgh Festival Fringe:
 
“My husband is allergic to rice…he’s Basmatic.”
Shappi Khorsandi - Carry On Shappi, Pleasance Dome
 
Shaparak “Shappi” Khorsandi is a British comedian and author of Iranian origin. “I’m allergic to rice. I’m basmatic” was posted on Twitter on April 29, 2009. “My mate’s allergic to rice. He’s basmatic” was posted on Twitter by Shappi Khorsandi‏ on November 16, 2009. “My friend is allergic to rice. He’s basmatic” was posted on Twitter on December 26, 2009.
 
     
Wikipedia: Basmati
Basmati (pronounced IPA: [baːsmət̪iː] in South Asia) is a variety of long, slender-grained aromatic rice which is traditionally from the Indian subcontinent. As of 2014, India exported 59 percent of the overseas basmati rice market, while Pakistan accounted for the remainder, according to the state-run Agricultural and Processed Food Products Export Development Authority. However, many countries use domestically grown basmati rice crops.
 
Wikipedia: Shappi Khorsandi
Shaparak “Shappi” Khorsandi (Persian: شاپرک خرسندی‎, born 8 June 1973) is a British comedian and author of Iranian origin. The daughter of the Iranian satirist and poet Hadi Khorsandi, she left Iran as a child following the Islamic Revolution.
         
26 August 2007, Sunday Mail (Glasgow, Scotland), “Best of the Fest of One-liners” by Steve Hendry, pg. 16:
EDINBURGH has been rocking with laughter for the past three weeks as the 2007 Fringe Festival has paid host to 675 comedy shows.
(...)
My husband is allergic to rice…he’s Basmatic.
Shappi Khorsandi - Carry On Shappi, Pleasance Dome
 
Twitter
JJ Timson‏
@jjtimson
I’m allergic to rice.
I’m basmatic.
4:40 PM - 29 Apr 2009
 
Twitter
Jon Pear‏
@neuroaster
RT @FunnyJoker ~ I’m allergic to rice. I’m basmatic. [and I’m alergic to vinegar-dressing - I’m balsamic]
9:40 AM - 3 May 2009
 
Twitter
Shamrock‏
@Shambo
From Shamster’s Fictionary: Basmatic - Allergic to rice.
3:54 PM - 17 Aug 2009
   
Twitter
Shappi Khorsandi‏
@ShappiKhorsandi
My mate’s allergic to rice. He’smatic. (TM @damncold68) I mean BASMATIC. Stupid keyboard messing with my flow.
4:05 AM - 16 Nov 2009
     
19 December 2009, The Guardian (London, UK), “Weekend: Pull the other one: Cracker jokes are notoriously terrible, so we challenged top comedians to do better,” pg. 16:
My mate’s allergic to rice. . . He’s basmatic.
Shappi Khorsandi
 
Twitter
Anne Marie Cunningham‏
@amcunningham
my mate’s allergic to rice. he’s basmatic.#guardianxmascrackerjokes
6:02 PM - 19 Dec 2009
   
Twitter
Jonathan‏
@jbjon
“My friend is allergic to rice. He’s basmatic” #crackerjokes
9:41 AM - 26 Dec 2009
         
Google Books
The Mammoth Book of One-Liners
Edited by Geoff Tibballs
London, UK: Constable & Robinson Ltd
2012
Pg. ?:
My friend’s allergic to rice. He’s basmatic.
 
Google Books
Crap Dad Jokes:
Because Dads aren’t as funny as they think they are
By Ian Allen
London, UK: Portico Books
2013
Pg. ?:
Patient: Doctor, I think I’m allergic to rice.
Doctor: You must be basmatic
 
Twitter
Shit Jokes‏
@ShitJokes
My friend’s allergic to rice.
He’s basmatic.
11:28 AM - 24 Jan 2016
     
The Guardian (London, UK)
Shappi Khorsandi: ‘My worst job? Life modelling for a woman who made me recite Shakespeare as I posed’
The comedian and author on memories of Iran, doing things her way and buying her mum a walk-on part
Rosanna Greenstreet
Sat 18 Feb 2017 04.30 EST Last modified on Fri 1 Dec 2017 10.23 EST
(...)
Tell us a joke
My mate’s allergic to rice. He’s basmatic.
 
Twitter
Shit Jokes‏
@ShitJokes
My friend’s allergic to rice.
He’s basmatic.
1:07 PM - 18 Jan 2018